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Mirrors > Home > ILE Home > Th. List > equequ2 | Unicode version |
Description: An equivalence law for equality. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
equequ2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equtrr 1703 | . 2 | |
2 | equtrr 1703 | . . 3 | |
3 | 2 | equcoms 1701 | . 2 |
4 | 1, 3 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 |
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-gen 1442 ax-ie2 1487 ax-8 1497 ax-17 1519 ax-i9 1523 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: ax11v2 1813 ax11v 1820 ax11ev 1821 equs5or 1823 eujust 2021 euf 2024 mo23 2060 eleq1w 2231 cbvabw 2293 csbcow 3060 disjiun 3984 iotaval 5171 dffun4f 5214 dff13f 5749 supmoti 6970 isoti 6984 nninfwlpoim 7154 exmidontriim 7202 ennnfonelemr 12378 ctinf 12385 infpn2 12411 |
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