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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 2142 |
. 2
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2 | eqtr 2158 |
. 2
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3 | 1, 2 | sylanb 282 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-4 1488 ax-17 1507 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-cleq 2133 |
This theorem is referenced by: eqvinc 2812 eqvincg 2813 moop2 4181 reusv3i 4388 relop 4697 f0rn0 5325 fliftfun 5705 th3qlem1 6539 enq0ref 7265 enq0tr 7266 genpdisj 7355 addlsub 8156 fsum2dlemstep 11235 0dvds 11549 cncongr1 11820 |
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