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Theorem syl5reqr 2103
Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.)
Hypotheses
Ref Expression
syl5reqr.1 𝐵 = 𝐴
syl5reqr.2 (𝜑𝐵 = 𝐶)
Assertion
Ref Expression
syl5reqr (𝜑𝐶 = 𝐴)

Proof of Theorem syl5reqr
StepHypRef Expression
1 syl5reqr.1 . . 3 𝐵 = 𝐴
21eqcomi 2060 . 2 𝐴 = 𝐵
3 syl5reqr.2 . 2 (𝜑𝐵 = 𝐶)
42, 3syl5req 2101 1 (𝜑𝐶 = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = 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:  bm2.5ii  4250  f1o00  5189  fmpt  5347  fmptsn  5380  resfunexg  5410  prarloclem5  6656  recexprlem1ssl  6789  recexprlem1ssu  6790  iooval2  8885  resqrexlemover  9837
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