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Mirrors > Home > ILE Home > Th. List > eqtr2 | Unicode version |
Description: A transitive law for class equality. (Contributed by NM, 20-May-2005.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
eqtr2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom 2159 | . 2 | |
2 | eqtr 2175 | . 2 | |
3 | 1, 2 | sylanb 282 | 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: eqvinc 2835 eqvincg 2836 moop2 4212 reusv3i 4420 relop 4737 f0rn0 5365 fliftfun 5747 th3qlem1 6583 enq0ref 7354 enq0tr 7355 genpdisj 7444 addlsub 8246 fsum2dlemstep 11335 0dvds 11711 cncongr1 11984 |
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