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Theorem syl5req 2130
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 2129 . 2 (𝜑𝐴 = 𝐶)
43eqcomd 2090 1 (𝜑𝐶 = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1287
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 1379  ax-gen 1381  ax-4 1443  ax-17 1462  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-cleq 2078
This theorem is referenced by:  syl5reqr  2132  opeqsn  4053  dcextest  4369  relop  4554  funopg  5013  funcnvres  5052  mapsnconst  6403  snexxph  6608  apreap  8005  recextlem1  8059  nn0supp  8658  intqfrac2  9654  hashprg  10113  hashfacen  10138
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