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Mirrors > Home > ILE Home > Th. List > notrab | Unicode version |
Description: Complementation of restricted class abstractions. (Contributed by Mario Carneiro, 3-Sep-2015.) |
Ref | Expression |
---|---|
notrab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difab 3233 | . 2 | |
2 | difin 3201 | . . 3 | |
3 | dfrab3 3240 | . . . 4 | |
4 | 3 | difeq2i 3087 | . . 3 |
5 | abid2 2199 | . . . 4 | |
6 | 5 | difeq1i 3086 | . . 3 |
7 | 2, 4, 6 | 3eqtr4i 2111 | . 2 |
8 | df-rab 2357 | . 2 | |
9 | 1, 7, 8 | 3eqtr4i 2111 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 102 wceq 1284 wcel 1433 cab 2067 crab 2352 cdif 2970 cin 2972 |
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-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rab 2357 df-v 2603 df-dif 2975 df-in 2979 |
This theorem is referenced by: diffitest 6371 |
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