Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > csbfv12gALTVD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of csbfv12gALTOLD 39052.
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.
csbfv12gALTOLD 39052 is csbfv12gALTVD 39135 without virtual deductions and was
automatically derived from csbfv12gALTVD 39135.
|
Ref | Expression |
---|---|
csbfv12gALTVD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idn1 38790 | . . . . . . . . . . 11 | |
2 | sbceqg 3984 | . . . . . . . . . . 11 | |
3 | 1, 2 | e1a 38852 | . . . . . . . . . 10 |
4 | csbima12 5483 | . . . . . . . . . . . . . 14 | |
5 | 4 | a1i 11 | . . . . . . . . . . . . 13 |
6 | 1, 5 | e1a 38852 | . . . . . . . . . . . 12 |
7 | csbsng 4243 | . . . . . . . . . . . . . 14 | |
8 | 1, 7 | e1a 38852 | . . . . . . . . . . . . 13 |
9 | imaeq2 5462 | . . . . . . . . . . . . 13 | |
10 | 8, 9 | e1a 38852 | . . . . . . . . . . . 12 |
11 | eqeq1 2626 | . . . . . . . . . . . . 13 | |
12 | 11 | biimprd 238 | . . . . . . . . . . . 12 |
13 | 6, 10, 12 | e11 38913 | . . . . . . . . . . 11 |
14 | csbconstg 3546 | . . . . . . . . . . . 12 | |
15 | 1, 14 | e1a 38852 | . . . . . . . . . . 11 |
16 | eqeq12 2635 | . . . . . . . . . . . 12 | |
17 | 16 | ex 450 | . . . . . . . . . . 11 |
18 | 13, 15, 17 | e11 38913 | . . . . . . . . . 10 |
19 | bibi1 341 | . . . . . . . . . . 11 | |
20 | 19 | biimprd 238 | . . . . . . . . . 10 |
21 | 3, 18, 20 | e11 38913 | . . . . . . . . 9 |
22 | 21 | gen11 38841 | . . . . . . . 8 |
23 | abbi 2737 | . . . . . . . . 9 | |
24 | 23 | biimpi 206 | . . . . . . . 8 |
25 | 22, 24 | e1a 38852 | . . . . . . 7 |
26 | csbab 4008 | . . . . . . . . 9 | |
27 | 26 | a1i 11 | . . . . . . . 8 |
28 | 1, 27 | e1a 38852 | . . . . . . 7 |
29 | eqeq2 2633 | . . . . . . . 8 | |
30 | 29 | biimpd 219 | . . . . . . 7 |
31 | 25, 28, 30 | e11 38913 | . . . . . 6 |
32 | unieq 4444 | . . . . . 6 | |
33 | 31, 32 | e1a 38852 | . . . . 5 |
34 | csbuni 4466 | . . . . . . 7 | |
35 | 34 | a1i 11 | . . . . . 6 |
36 | 1, 35 | e1a 38852 | . . . . 5 |
37 | eqeq2 2633 | . . . . . 6 | |
38 | 37 | biimpd 219 | . . . . 5 |
39 | 33, 36, 38 | e11 38913 | . . . 4 |
40 | dffv4 6188 | . . . . . 6 | |
41 | 40 | ax-gen 1722 | . . . . 5 |
42 | csbeq2 3537 | . . . . . 6 | |
43 | 42 | a1i 11 | . . . . 5 |
44 | 1, 41, 43 | e10 38919 | . . . 4 |
45 | eqeq2 2633 | . . . . 5 | |
46 | 45 | biimpd 219 | . . . 4 |
47 | 39, 44, 46 | e11 38913 | . . 3 |
48 | dffv4 6188 | . . 3 | |
49 | eqeq2 2633 | . . . 4 | |
50 | 49 | biimprcd 240 | . . 3 |
51 | 47, 48, 50 | e10 38919 | . 2 |
52 | 51 | in1 38787 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wceq 1483 wcel 1990 cab 2608 wsbc 3435 csb 3533 csn 4177 cuni 4436 cima 5117 cfv 5888 |
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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-fal 1489 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fv 5896 df-vd1 38786 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |