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Mirrors > Home > ILE Home > Th. List > eqtr | Unicode version |
Description: Transitive law for class equality. Proposition 4.7(3) of [TakeutiZaring] p. 13. (Contributed by NM, 25-Jan-2004.) |
Ref | Expression |
---|---|
eqtr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2164 | . 2 | |
2 | 1 | biimpar 295 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 |
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 1427 ax-gen 1429 ax-4 1490 ax-17 1506 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-cleq 2150 |
This theorem is referenced by: eqtr2 2176 eqtr3 2177 sylan9eq 2210 eqvinc 2835 eqvincg 2836 uneqdifeqim 3479 preqsn 3738 dtruex 4518 relresfld 5115 relcoi1 5117 eqer 6512 xpider 6551 addlsub 8245 bj-findis 13554 |
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