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Theorem syl6req 2086
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 2085 . 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:  syl6reqr  2088  elxp4  4751  elxp5  4752  fo1stresm  5730  fo2ndresm  5731  eloprabi  5764  fo2ndf  5790  xpsnen  6231  xpassen  6240  ine0  7147  nn0n0n1ge2  8047  fzval2  8607  fseq1p1m1  8686
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