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Mirrors > Home > ILE Home > Th. List > difjust | Unicode version |
Description: Soundness justification theorem for df-dif 2975. (Contributed by Rodolfo Medina, 27-Apr-2010.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
difjust |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2141 | . . . 4 | |
2 | eleq1 2141 | . . . . 5 | |
3 | 2 | notbid 624 | . . . 4 |
4 | 1, 3 | anbi12d 456 | . . 3 |
5 | 4 | cbvabv 2202 | . 2 |
6 | eleq1 2141 | . . . 4 | |
7 | eleq1 2141 | . . . . 5 | |
8 | 7 | notbid 624 | . . . 4 |
9 | 6, 8 | anbi12d 456 | . . 3 |
10 | 9 | cbvabv 2202 | . 2 |
11 | 5, 10 | eqtri 2101 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 102 wceq 1284 wcel 1433 cab 2067 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 |
This theorem is referenced by: (None) |
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