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Mirrors > Home > NFE Home > Th. List > eleq12 | Unicode version |
Description: Equality implies equivalence of membership. (Contributed by NM, 31-May-1999.) |
Ref | Expression |
---|---|
eleq12 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2413 |
. 2
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2 | eleq2 2414 |
. 2
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3 | 1, 2 | sylan9bb 680 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-cleq 2346 df-clel 2349 |
This theorem is referenced by: nnsucelr 4429 ncfinlower 4484 sfindbl 4531 |
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