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Mirrors > Home > ILE Home > Th. List > difjust | Unicode version |
Description: Soundness justification theorem for df-dif 3078. (Contributed by Rodolfo Medina, 27-Apr-2010.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
difjust |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2203 | . . . 4 | |
2 | eleq1 2203 | . . . . 5 | |
3 | 2 | notbid 657 | . . . 4 |
4 | 1, 3 | anbi12d 465 | . . 3 |
5 | 4 | cbvabv 2265 | . 2 |
6 | eleq1 2203 | . . . 4 | |
7 | eleq1 2203 | . . . . 5 | |
8 | 7 | notbid 657 | . . . 4 |
9 | 6, 8 | anbi12d 465 | . . 3 |
10 | 9 | cbvabv 2265 | . 2 |
11 | 5, 10 | eqtri 2161 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wceq 1332 wcel 1481 cab 2126 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 |
This theorem is referenced by: (None) |
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