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Mirrors > Home > MPE Home > Th. List > Mathboxes > csbrngVD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of csbrngOLD 39056.
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.
csbrngOLD 39056 is csbrngVD 39132 without virtual deductions and was
automatically derived from csbrngVD 39132.
|
Ref | Expression |
---|---|
csbrngVD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idn1 38790 | . . . . . . . . . . . 12 | |
2 | sbcel12gOLD 38754 | . . . . . . . . . . . 12 | |
3 | 1, 2 | e1a 38852 | . . . . . . . . . . 11 |
4 | csbconstg 3546 | . . . . . . . . . . . . 13 | |
5 | 1, 4 | e1a 38852 | . . . . . . . . . . . 12 |
6 | eleq1 2689 | . . . . . . . . . . . 12 | |
7 | 5, 6 | e1a 38852 | . . . . . . . . . . 11 |
8 | bibi1 341 | . . . . . . . . . . . 12 | |
9 | 8 | biimprd 238 | . . . . . . . . . . 11 |
10 | 3, 7, 9 | e11 38913 | . . . . . . . . . 10 |
11 | 10 | gen11 38841 | . . . . . . . . 9 |
12 | exbi 1773 | . . . . . . . . 9 | |
13 | 11, 12 | e1a 38852 | . . . . . . . 8 |
14 | sbcexgOLD 38753 | . . . . . . . . . 10 | |
15 | 14 | bicomd 213 | . . . . . . . . 9 |
16 | 1, 15 | e1a 38852 | . . . . . . . 8 |
17 | bitr3 342 | . . . . . . . . 9 | |
18 | 17 | com12 32 | . . . . . . . 8 |
19 | 13, 16, 18 | e11 38913 | . . . . . . 7 |
20 | 19 | gen11 38841 | . . . . . 6 |
21 | abbi 2737 | . . . . . . 7 | |
22 | 21 | biimpi 206 | . . . . . 6 |
23 | 20, 22 | e1a 38852 | . . . . 5 |
24 | csbabgOLD 39050 | . . . . . 6 | |
25 | 1, 24 | e1a 38852 | . . . . 5 |
26 | eqeq2 2633 | . . . . . 6 | |
27 | 26 | biimpd 219 | . . . . 5 |
28 | 23, 25, 27 | e11 38913 | . . . 4 |
29 | dfrn3 5312 | . . . . . 6 | |
30 | 29 | ax-gen 1722 | . . . . 5 |
31 | csbeq2gOLD 38765 | . . . . 5 | |
32 | 1, 30, 31 | e10 38919 | . . . 4 |
33 | eqeq2 2633 | . . . . 5 | |
34 | 33 | biimpd 219 | . . . 4 |
35 | 28, 32, 34 | e11 38913 | . . 3 |
36 | dfrn3 5312 | . . 3 | |
37 | eqeq2 2633 | . . . 4 | |
38 | 37 | biimprcd 240 | . . 3 |
39 | 35, 36, 38 | e10 38919 | . 2 |
40 | 39 | in1 38787 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wceq 1483 wex 1704 wcel 1990 cab 2608 wsbc 3435 csb 3533 cop 4183 crn 5115 |
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 ax-nul 4789 ax-pr 4906 |
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-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 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-br 4654 df-opab 4713 df-cnv 5122 df-dm 5124 df-rn 5125 df-vd1 38786 |
This theorem is referenced by: (None) |
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