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Mirrors > Home > ILE Home > Th. List > eleq12i | Unicode version |
Description: Inference from equality to equivalence of membership. (Contributed by NM, 31-May-1994.) |
Ref | Expression |
---|---|
eleq1i.1 | |
eleq12i.2 |
Ref | Expression |
---|---|
eleq12i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq12i.2 | . . 3 | |
2 | 1 | eleq2i 2104 | . 2 |
3 | eleq1i.1 | . . 3 | |
4 | 3 | eleq1i 2103 | . 2 |
5 | 2, 4 | bitri 173 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 98 wceq 1243 wcel 1393 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-clel 2036 |
This theorem is referenced by: 3eltr3g 2122 3eltr4g 2123 sbcel12g 2865 |
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