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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 2181 | . . . 4 | |
2 | 1 | notbid 641 | . . 3 |
3 | 2 | rabbidv 2649 | . 2 |
4 | dfdif2 3049 | . 2 | |
5 | dfdif2 3049 | . 2 | |
6 | 3, 4, 5 | 3eqtr4g 2175 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1316 wcel 1465 crab 2397 cdif 3038 |
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 588 ax-in2 589 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-ral 2398 df-rab 2402 df-dif 3043 |
This theorem is referenced by: difeq12 3159 difeq2i 3161 difeq2d 3164 disjdif2 3411 ssdifeq0 3415 2oconcl 6304 diffitest 6749 diffifi 6756 undifdc 6780 sbthlem2 6814 isbth 6823 difinfinf 6954 ismkvnex 6997 iscld 12199 |
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