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Mirrors > Home > ILE Home > Th. List > rabbi | Unicode version |
Description: Equivalent wff's correspond to equal restricted class abstractions. Closed theorem form of rabbidva 2674. (Contributed by NM, 25-Nov-2013.) |
Ref | Expression |
---|---|
rabbi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abbi 2253 | . 2 | |
2 | df-ral 2421 | . . 3 | |
3 | pm5.32 448 | . . . 4 | |
4 | 3 | albii 1446 | . . 3 |
5 | 2, 4 | bitri 183 | . 2 |
6 | df-rab 2425 | . . 3 | |
7 | df-rab 2425 | . . 3 | |
8 | 6, 7 | eqeq12i 2153 | . 2 |
9 | 1, 5, 8 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wcel 1480 cab 2125 wral 2416 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-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-ral 2421 df-rab 2425 |
This theorem is referenced by: rabbidva 2674 exmidonfinlem 7049 |
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