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Theorem eqtr2d 2055
Description: An equality transitivity deduction. (Contributed by NM, 18-Oct-1999.)
Hypotheses
Ref Expression
eqtr2d.1 (φA = B)
eqtr2d.2 (φB = 𝐶)
Assertion
Ref Expression
eqtr2d (φ𝐶 = A)

Proof of Theorem eqtr2d
StepHypRef Expression
1 eqtr2d.1 . . 3 (φA = B)
2 eqtr2d.2 . . 3 (φB = 𝐶)
31, 2eqtrd 2054 . 2 (φA = 𝐶)
43eqcomd 2027 1 (φ𝐶 = A)
Colors of variables: wff set class
Syntax hints:  wi 4   = 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:  3eqtrrd  2059  3eqtr2rd  2061  onsucmin  4182  elxp4  4735  elxp5  4736  csbopeq1a  5737  ecinxp  6092  1idsr  6515  cnegexlem3  6775  cnegex  6776  submul2  6982  mulsubfacd  7001
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