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Mirrors > Home > MPE Home > Th. List > Mathboxes > onfrALTlem5VD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of onfrALTlem5 38757.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
onfrALTlem5 38757 is onfrALTlem5VD 39121 without virtual deductions and was
automatically derived from onfrALTlem5VD 39121.
|
Ref | Expression |
---|---|
onfrALTlem5VD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3203 | . . . 4 | |
2 | 1 | inex1 4799 | . . 3 |
3 | sbcimg 3477 | . . 3 | |
4 | 2, 3 | e0a 38999 | . 2 |
5 | sbcangOLD 38739 | . . . . 5 | |
6 | 2, 5 | e0a 38999 | . . . 4 |
7 | sseq1 3626 | . . . . . . 7 | |
8 | 7 | sbcieg 3468 | . . . . . 6 |
9 | 2, 8 | e0a 38999 | . . . . 5 |
10 | sbcng 3476 | . . . . . . . . 9 | |
11 | 10 | bicomd 213 | . . . . . . . 8 |
12 | 2, 11 | e0a 38999 | . . . . . . 7 |
13 | df-ne 2795 | . . . . . . . . 9 | |
14 | 13 | ax-gen 1722 | . . . . . . . 8 |
15 | sbcbi 38749 | . . . . . . . 8 | |
16 | 2, 14, 15 | e00 38995 | . . . . . . 7 |
17 | 12, 16 | bitr4i 267 | . . . . . 6 |
18 | eqsbc3 3475 | . . . . . . . . 9 | |
19 | 2, 18 | e0a 38999 | . . . . . . . 8 |
20 | 19 | notbii 310 | . . . . . . 7 |
21 | df-ne 2795 | . . . . . . 7 | |
22 | 20, 21 | bitr4i 267 | . . . . . 6 |
23 | 17, 22 | bitr3i 266 | . . . . 5 |
24 | 9, 23 | anbi12i 733 | . . . 4 |
25 | 6, 24 | bitri 264 | . . 3 |
26 | df-rex 2918 | . . . . . 6 | |
27 | 26 | ax-gen 1722 | . . . . 5 |
28 | sbcbi 38749 | . . . . 5 | |
29 | 2, 27, 28 | e00 38995 | . . . 4 |
30 | sbcexgOLD 38753 | . . . . . . 7 | |
31 | 30 | bicomd 213 | . . . . . 6 |
32 | 2, 31 | e0a 38999 | . . . . 5 |
33 | sbcangOLD 38739 | . . . . . . . . . 10 | |
34 | 2, 33 | e0a 38999 | . . . . . . . . 9 |
35 | sbcel2gv 3496 | . . . . . . . . . . 11 | |
36 | 2, 35 | e0a 38999 | . . . . . . . . . 10 |
37 | sbceqg 3984 | . . . . . . . . . . . 12 | |
38 | 2, 37 | e0a 38999 | . . . . . . . . . . 11 |
39 | csbingOLD 39054 | . . . . . . . . . . . . . 14 | |
40 | 2, 39 | e0a 38999 | . . . . . . . . . . . . 13 |
41 | csbvarg 4003 | . . . . . . . . . . . . . . 15 | |
42 | 2, 41 | e0a 38999 | . . . . . . . . . . . . . 14 |
43 | csbconstg 3546 | . . . . . . . . . . . . . . 15 | |
44 | 2, 43 | e0a 38999 | . . . . . . . . . . . . . 14 |
45 | 42, 44 | ineq12i 3812 | . . . . . . . . . . . . 13 |
46 | 40, 45 | eqtri 2644 | . . . . . . . . . . . 12 |
47 | csbconstg 3546 | . . . . . . . . . . . . 13 | |
48 | 2, 47 | e0a 38999 | . . . . . . . . . . . 12 |
49 | 46, 48 | eqeq12i 2636 | . . . . . . . . . . 11 |
50 | 38, 49 | bitri 264 | . . . . . . . . . 10 |
51 | 36, 50 | anbi12i 733 | . . . . . . . . 9 |
52 | 34, 51 | bitri 264 | . . . . . . . 8 |
53 | 52 | ax-gen 1722 | . . . . . . 7 |
54 | exbi 1773 | . . . . . . 7 | |
55 | 53, 54 | e0a 38999 | . . . . . 6 |
56 | df-rex 2918 | . . . . . 6 | |
57 | 55, 56 | bitr4i 267 | . . . . 5 |
58 | 32, 57 | bitr3i 266 | . . . 4 |
59 | 29, 58 | bitri 264 | . . 3 |
60 | 25, 59 | imbi12i 340 | . 2 |
61 | 4, 60 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wa 384 wal 1481 wceq 1483 wex 1704 wcel 1990 wne 2794 wrex 2913 cvv 3200 wsbc 3435 csb 3533 cin 3573 wss 3574 c0 3915 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-in 3581 df-ss 3588 |
This theorem is referenced by: (None) |
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