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Theorem eqtr2 2055
Description: A transitive law for class equality. (Contributed by NM, 20-May-2005.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
eqtr2 ((A = B A = 𝐶) → B = 𝐶)

Proof of Theorem eqtr2
StepHypRef Expression
1 eqcom 2039 . 2 (A = BB = A)
2 eqtr 2054 . 2 ((B = A A = 𝐶) → B = 𝐶)
31, 2sylanb 268 1 ((A = B A = 𝐶) → B = 𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   = wceq 1242
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030
This theorem is referenced by:  eqvinc  2661  eqvincg  2662  moop2  3979  reusv3i  4157  relop  4429  fliftfun  5379  th3qlem1  6144  enq0ref  6415  enq0tr  6416  genpdisj  6506
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