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Theorem syl5reqr 2084
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 2041 . 2 A = B
3 syl5reqr.2 . 2 (φB = 𝐶)
42, 3syl5req 2082 1 (φ𝐶 = A)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242
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 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030
This theorem is referenced by:  bm2.5ii  4188  f1o00  5104  fmpt  5262  fmptsn  5295  resfunexg  5325  prarloclem5  6482  recexprlem1ssl  6604  recexprlem1ssu  6605  iooval2  8534
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