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Theorem eqtr2 2040
 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 2024 . 2 (A = BB = A)
2 eqtr 2039 . 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 1228 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 1316  ax-gen 1318  ax-4 1381  ax-17 1400  ax-ext 2004 This theorem depends on definitions:  df-bi 110  df-cleq 2015 This theorem is referenced by:  eqvinc  2644  eqvincg  2645  moop2  3962  reusv3i  4141  relop  4413  fliftfun  5361  th3qlem1  6119  enq0ref  6288  enq0tr  6289  genpdisj  6378
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