Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > sbc3orgVD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of sbc3orgOLD 38742. The following user's proof is
completed by invoking mmj2's unify command and using mmj2's StepSelector
to pick all remaining steps of the Metamath proof.
|
Ref | Expression |
---|---|
sbc3orgVD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idn1 38790 | . . . . . 6 | |
2 | sbcorgOLD 38740 | . . . . . 6 | |
3 | 1, 2 | e1a 38852 | . . . . 5 |
4 | df-3or 1038 | . . . . . . . . 9 | |
5 | 4 | bicomi 214 | . . . . . . . 8 |
6 | 5 | ax-gen 1722 | . . . . . . 7 |
7 | spsbc 3448 | . . . . . . 7 | |
8 | 1, 6, 7 | e10 38919 | . . . . . 6 |
9 | sbcbig 3480 | . . . . . . 7 | |
10 | 9 | biimpd 219 | . . . . . 6 |
11 | 1, 8, 10 | e11 38913 | . . . . 5 |
12 | bitr3 342 | . . . . . 6 | |
13 | 12 | com12 32 | . . . . 5 |
14 | 3, 11, 13 | e11 38913 | . . . 4 |
15 | sbcorgOLD 38740 | . . . . . 6 | |
16 | 1, 15 | e1a 38852 | . . . . 5 |
17 | orbi1 742 | . . . . 5 | |
18 | 16, 17 | e1a 38852 | . . . 4 |
19 | bibi1 341 | . . . . 5 | |
20 | 19 | biimprd 238 | . . . 4 |
21 | 14, 18, 20 | e11 38913 | . . 3 |
22 | df-3or 1038 | . . . 4 | |
23 | 22 | bicomi 214 | . . 3 |
24 | bibi1 341 | . . . 4 | |
25 | 24 | biimprd 238 | . . 3 |
26 | 21, 23, 25 | e10 38919 | . 2 |
27 | 26 | in1 38787 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wo 383 w3o 1036 wal 1481 wcel 1990 wsbc 3435 |
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-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 df-sbc 3436 df-vd1 38786 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |