Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2200 | . 2 | |
2 | eleq2 2201 | . 2 | |
3 | 1, 2 | sylan9bb 457 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 |
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-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-cleq 2130 df-clel 2133 |
This theorem is referenced by: trel 4028 pwnss 4078 epelg 4207 preleq 4465 acexmid 5766 cldval 12257 |
Copyright terms: Public domain | W3C validator |