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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom 2179 |
. 2
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2 | eqtr 2195 |
. 2
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3 | 1, 2 | sylanb 284 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-4 1510 ax-17 1526 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 |
This theorem is referenced by: eqvinc 2860 eqvincg 2861 moop2 4251 reusv3i 4459 relop 4777 f0rn0 5410 fliftfun 5796 th3qlem1 6636 enq0ref 7431 enq0tr 7432 genpdisj 7521 addlsub 8326 fsum2dlemstep 11441 0dvds 11817 cncongr1 12102 |
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