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Theorem eqtr2 2074
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 = 𝐵𝐴 = 𝐶) → 𝐵 = 𝐶)

Proof of Theorem eqtr2
StepHypRef Expression
1 eqcom 2058 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
2 eqtr 2073 . 2 ((𝐵 = 𝐴𝐴 = 𝐶) → 𝐵 = 𝐶)
31, 2sylanb 272 1 ((𝐴 = 𝐵𝐴 = 𝐶) → 𝐵 = 𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101   = wceq 1259
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-4 1416  ax-17 1435  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049
This theorem is referenced by:  eqvinc  2689  eqvincg  2690  moop2  4015  reusv3i  4218  relop  4513  fliftfun  5463  th3qlem1  6238  enq0ref  6588  enq0tr  6589  genpdisj  6678  addlsub  7439  0dvds  10127
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