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Mirrors > Home > MPE Home > Th. List > Mathboxes > csbunigVD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of csbunigOLD 39051.
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.
csbunigOLD 39051 is csbunigVD 39134 without virtual deductions and was
automatically derived from csbunigVD 39134.
|
Ref | Expression |
---|---|
csbunigVD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idn1 38790 | . . . . . . . . . . . . 13 | |
2 | sbcg 3503 | . . . . . . . . . . . . 13 | |
3 | 1, 2 | e1a 38852 | . . . . . . . . . . . 12 |
4 | sbcel2gOLD 38755 | . . . . . . . . . . . . 13 | |
5 | 1, 4 | e1a 38852 | . . . . . . . . . . . 12 |
6 | pm4.38 916 | . . . . . . . . . . . . 13 | |
7 | 6 | ex 450 | . . . . . . . . . . . 12 |
8 | 3, 5, 7 | e11 38913 | . . . . . . . . . . 11 |
9 | sbcangOLD 38739 | . . . . . . . . . . . 12 | |
10 | 1, 9 | e1a 38852 | . . . . . . . . . . 11 |
11 | bibi1 341 | . . . . . . . . . . . 12 | |
12 | 11 | biimprcd 240 | . . . . . . . . . . 11 |
13 | 8, 10, 12 | e11 38913 | . . . . . . . . . 10 |
14 | 13 | gen11 38841 | . . . . . . . . 9 |
15 | exbi 1773 | . . . . . . . . 9 | |
16 | 14, 15 | e1a 38852 | . . . . . . . 8 |
17 | sbcexgOLD 38753 | . . . . . . . . 9 | |
18 | 1, 17 | e1a 38852 | . . . . . . . 8 |
19 | bibi1 341 | . . . . . . . . 9 | |
20 | 19 | biimprcd 240 | . . . . . . . 8 |
21 | 16, 18, 20 | e11 38913 | . . . . . . 7 |
22 | 21 | gen11 38841 | . . . . . 6 |
23 | abbi 2737 | . . . . . . 7 | |
24 | 23 | biimpi 206 | . . . . . 6 |
25 | 22, 24 | e1a 38852 | . . . . 5 |
26 | csbabgOLD 39050 | . . . . . 6 | |
27 | 1, 26 | e1a 38852 | . . . . 5 |
28 | eqeq2 2633 | . . . . . 6 | |
29 | 28 | biimpd 219 | . . . . 5 |
30 | 25, 27, 29 | e11 38913 | . . . 4 |
31 | df-uni 4437 | . . . . . . 7 | |
32 | 31 | ax-gen 1722 | . . . . . 6 |
33 | spsbc 3448 | . . . . . 6 | |
34 | 1, 32, 33 | e10 38919 | . . . . 5 |
35 | sbceqg 3984 | . . . . . 6 | |
36 | 35 | biimpd 219 | . . . . 5 |
37 | 1, 34, 36 | e11 38913 | . . . 4 |
38 | eqeq2 2633 | . . . . 5 | |
39 | 38 | biimpd 219 | . . . 4 |
40 | 30, 37, 39 | e11 38913 | . . 3 |
41 | df-uni 4437 | . . 3 | |
42 | eqeq2 2633 | . . . 4 | |
43 | 42 | biimprcd 240 | . . 3 |
44 | 40, 41, 43 | e10 38919 | . 2 |
45 | 44 | in1 38787 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wceq 1483 wex 1704 wcel 1990 cab 2608 wsbc 3435 csb 3533 cuni 4436 |
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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 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-v 3202 df-sbc 3436 df-csb 3534 df-uni 4437 df-vd1 38786 |
This theorem is referenced by: (None) |
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