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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 2234 | . . . 4 | |
2 | 1 | notbid 662 | . . 3 |
3 | 2 | rabbidv 2719 | . 2 |
4 | dfdif2 3129 | . 2 | |
5 | dfdif2 3129 | . 2 | |
6 | 3, 4, 5 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1348 wcel 2141 crab 2452 cdif 3118 |
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 609 ax-in2 610 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-ral 2453 df-rab 2457 df-dif 3123 |
This theorem is referenced by: difeq12 3240 difeq2i 3242 difeq2d 3245 disjdif2 3492 ssdifeq0 3496 2oconcl 6416 diffitest 6863 diffifi 6870 undifdc 6899 sbthlem2 6933 isbth 6942 difinfinf 7076 ismkvnex 7129 iscld 12862 |
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