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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 1690 | . 2 | |
2 | equtrr 1690 | . . 3 | |
3 | 2 | equcoms 1688 | . 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 1429 ax-ie2 1474 ax-8 1484 ax-17 1506 ax-i9 1510 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: ax11v2 1800 ax11v 1807 ax11ev 1808 equs5or 1810 eujust 2008 euf 2011 mo23 2047 eleq1w 2218 cbvabw 2280 csbcow 3042 disjiun 3962 iotaval 5149 dffun4f 5189 dff13f 5723 supmoti 6940 isoti 6954 exmidontriim 7163 ennnfonelemr 12248 ctinf 12255 |
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