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Mirrors > Home > ILE Home > Th. List > eleq2w | Unicode version |
Description: Weaker version of eleq2 2234 (but more general than elequ2 2146) not depending on ax-ext 2152 nor df-cleq 2163. (Contributed by BJ, 29-Sep-2019.) |
Ref | Expression |
---|---|
eleq2w |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elequ2 2146 | . . . 4 | |
2 | 1 | anbi2d 461 | . . 3 |
3 | 2 | exbidv 1818 | . 2 |
4 | df-clel 2166 | . 2 | |
5 | df-clel 2166 | . 2 | |
6 | 3, 4, 5 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wex 1485 wcel 2141 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-14 2144 |
This theorem depends on definitions: df-bi 116 df-clel 2166 |
This theorem is referenced by: exmidontriimlem4 7188 |
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