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Mirrors > Home > NFE Home > Th. List > eleq12i | Unicode version |
Description: Inference from equality to equivalence of membership. (Contributed by NM, 31-May-1994.) |
Ref | Expression |
---|---|
eleq1i.1 |
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eleq12i.2 |
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Ref | Expression |
---|---|
eleq12i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq12i.2 |
. . 3
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2 | 1 | eleq2i 2417 |
. 2
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3 | eleq1i.1 |
. . 3
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4 | 3 | eleq1i 2416 |
. 2
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5 | 2, 4 | bitri 240 |
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: 3eltr3g 2435 3eltr4g 2436 sbcel12g 3152 |
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