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Theorem syl5req 2101
 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 2100 . 2 (𝜑𝐴 = 𝐶)
43eqcomd 2061 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:  syl5reqr  2103  opeqsn  4017  relop  4514  funopg  4962  funcnvres  5000  apreap  7652  recextlem1  7706  nn0supp  8291  intqfrac2  9269
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