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Theorem syl6req 2071
Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.)
Hypotheses
Ref Expression
syl6req.1 (φA = B)
syl6req.2 B = 𝐶
Assertion
Ref Expression
syl6req (φ𝐶 = A)

Proof of Theorem syl6req
StepHypRef Expression
1 syl6req.1 . . 3 (φA = B)
2 syl6req.2 . . 3 B = 𝐶
31, 2syl6eq 2070 . 2 (φA = 𝐶)
43eqcomd 2027 1 (φ𝐶 = A)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1228
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 1316  ax-gen 1318  ax-4 1381  ax-17 1400  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-cleq 2015
This theorem is referenced by:  syl6reqr  2073  elxp4  4735  elxp5  4736  fo1stresm  5711  fo2ndresm  5712  eloprabi  5745  fo2ndf  5771  ine0  6977
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