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Mirrors > Home > ILE Home > Th. List > rabeqf | Unicode version |
Description: Equality theorem for restricted class abstractions, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 7-Mar-2004.) |
Ref | Expression |
---|---|
rabeqf.1 | |
rabeqf.2 |
Ref | Expression |
---|---|
rabeqf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabeqf.1 | . . . 4 | |
2 | rabeqf.2 | . . . 4 | |
3 | 1, 2 | nfeq 2289 | . . 3 |
4 | eleq2 2203 | . . . 4 | |
5 | 4 | anbi1d 460 | . . 3 |
6 | 3, 5 | abbid 2256 | . 2 |
7 | df-rab 2425 | . 2 | |
8 | df-rab 2425 | . 2 | |
9 | 6, 7, 8 | 3eqtr4g 2197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 cab 2125 wnfc 2268 crab 2420 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 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-nfc 2270 df-rab 2425 |
This theorem is referenced by: rabeqif 2677 rabeq 2678 |
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