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Theorem syl5req 2082
Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.)
Hypotheses
Ref Expression
syl5req.1 A = B
syl5req.2 (φB = 𝐶)
Assertion
Ref Expression
syl5req (φ𝐶 = A)

Proof of Theorem syl5req
StepHypRef Expression
1 syl5req.1 . . 3 A = B
2 syl5req.2 . . 3 (φB = 𝐶)
31, 2syl5eq 2081 . 2 (φA = 𝐶)
43eqcomd 2042 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:  syl5reqr  2084  opeqsn  3980  relop  4429  funopg  4877  funcnvres  4915  apreap  7351  recextlem1  7394  nn0supp  7990
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