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Mirrors > Home > MPE Home > Th. List > Mathboxes > sbcssgVD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of sbcssg 4085.
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.
sbcssg 4085 is sbcssgVD 39119 without virtual deductions and was automatically
derived from sbcssgVD 39119.
|
Ref | Expression |
---|---|
sbcssgVD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idn1 38790 | . . . . . . . . . 10 | |
2 | sbcel2gOLD 38755 | . . . . . . . . . 10 | |
3 | 1, 2 | e1a 38852 | . . . . . . . . 9 |
4 | sbcel2gOLD 38755 | . . . . . . . . . 10 | |
5 | 1, 4 | e1a 38852 | . . . . . . . . 9 |
6 | imbi12 336 | . . . . . . . . 9 | |
7 | 3, 5, 6 | e11 38913 | . . . . . . . 8 |
8 | sbcimg 3477 | . . . . . . . . 9 | |
9 | 1, 8 | e1a 38852 | . . . . . . . 8 |
10 | bibi1 341 | . . . . . . . . 9 | |
11 | 10 | biimprcd 240 | . . . . . . . 8 |
12 | 7, 9, 11 | e11 38913 | . . . . . . 7 |
13 | 12 | gen11 38841 | . . . . . 6 |
14 | albi 1746 | . . . . . 6 | |
15 | 13, 14 | e1a 38852 | . . . . 5 |
16 | sbcalgOLD 38752 | . . . . . 6 | |
17 | 1, 16 | e1a 38852 | . . . . 5 |
18 | bibi1 341 | . . . . . 6 | |
19 | 18 | biimprcd 240 | . . . . 5 |
20 | 15, 17, 19 | e11 38913 | . . . 4 |
21 | dfss2 3591 | . . . . . 6 | |
22 | 21 | ax-gen 1722 | . . . . 5 |
23 | sbcbi 38749 | . . . . 5 | |
24 | 1, 22, 23 | e10 38919 | . . . 4 |
25 | bibi1 341 | . . . . 5 | |
26 | 25 | biimprcd 240 | . . . 4 |
27 | 20, 24, 26 | e11 38913 | . . 3 |
28 | dfss2 3591 | . . 3 | |
29 | biantr 972 | . . . 4 | |
30 | 29 | ex 450 | . . 3 |
31 | 27, 28, 30 | e10 38919 | . 2 |
32 | 31 | in1 38787 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wcel 1990 wsbc 3435 csb 3533 wss 3574 |
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-in 3581 df-ss 3588 df-vd1 38786 |
This theorem is referenced by: (None) |
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