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Theorem syl6req 2131
Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.)
Hypotheses
Ref Expression
syl6req.1 (𝜑𝐴 = 𝐵)
syl6req.2 𝐵 = 𝐶
Assertion
Ref Expression
syl6req (𝜑𝐶 = 𝐴)

Proof of Theorem syl6req
StepHypRef Expression
1 syl6req.1 . . 3 (𝜑𝐴 = 𝐵)
2 syl6req.2 . . 3 𝐵 = 𝐶
31, 2syl6eq 2130 . 2 (𝜑𝐴 = 𝐶)
43eqcomd 2087 1 (𝜑𝐶 = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-cleq 2075
This theorem is referenced by:  syl6reqr  2133  elxp4  4838  elxp5  4839  fo1stresm  5819  fo2ndresm  5820  eloprabi  5853  fo2ndf  5879  xpsnen  6365  xpassen  6374  ac6sfi  6431  undiffi  6443  ine0  7565  nn0n0n1ge2  8499  fzval2  9108  fseq1p1m1  9187  odd2np1  10417  sqpweven  10697  2sqpwodd  10698
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