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Mirrors > Home > ILE Home > Th. List > difeq2 | Unicode version |
Description: Equality theorem for class difference. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
difeq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2203 | . . . 4 | |
2 | 1 | notbid 656 | . . 3 |
3 | 2 | rabbidv 2675 | . 2 |
4 | dfdif2 3079 | . 2 | |
5 | dfdif2 3079 | . 2 | |
6 | 3, 4, 5 | 3eqtr4g 2197 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1331 wcel 1480 crab 2420 cdif 3068 |
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 603 ax-in2 604 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-ral 2421 df-rab 2425 df-dif 3073 |
This theorem is referenced by: difeq12 3189 difeq2i 3191 difeq2d 3194 disjdif2 3441 ssdifeq0 3445 2oconcl 6336 diffitest 6781 diffifi 6788 undifdc 6812 sbthlem2 6846 isbth 6855 difinfinf 6986 ismkvnex 7029 iscld 12272 |
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