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Mirrors > Home > ILE Home > Th. List > eleq12 | Unicode version |
Description: Equality implies equivalence of membership. (Contributed by NM, 31-May-1999.) |
Ref | Expression |
---|---|
eleq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2220 | . 2 | |
2 | eleq2 2221 | . 2 | |
3 | 1, 2 | sylan9bb 458 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wcel 2128 |
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 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-4 1490 ax-17 1506 ax-ial 1514 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-cleq 2150 df-clel 2153 |
This theorem is referenced by: trel 4070 pwnss 4121 epelg 4251 preleq 4515 acexmid 5824 cldval 12541 |
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