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Theorem eqtr3 2037
Description: A transitive law for class equality. (Contributed by NM, 20-May-2005.)
Assertion
Ref Expression
eqtr3 ((A = 𝐶 B = 𝐶) → A = B)

Proof of Theorem eqtr3
StepHypRef Expression
1 eqcom 2020 . 2 (B = 𝐶𝐶 = B)
2 eqtr 2035 . 2 ((A = 𝐶 𝐶 = B) → A = B)
31, 2sylan2b 271 1 ((A = 𝐶 B = 𝐶) → A = B)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   = wceq 1226
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 1312  ax-gen 1314  ax-4 1377  ax-17 1396  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-cleq 2011
This theorem is referenced by:  eueq  2685  euind  2701  reuind  2717  preqsn  3516  eusv1  4130  funopg  4856  foco  5037  mpt2fun  5522  enq0tr  6283
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