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Theorem syl6reqr 2133
Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.)
Hypotheses
Ref Expression
syl6reqr.1  |-  ( ph  ->  A  =  B )
syl6reqr.2  |-  C  =  B
Assertion
Ref Expression
syl6reqr  |-  ( ph  ->  C  =  A )

Proof of Theorem syl6reqr
StepHypRef Expression
1 syl6reqr.1 . 2  |-  ( ph  ->  A  =  B )
2 syl6reqr.2 . . 3  |-  C  =  B
32eqcomi 2086 . 2  |-  B  =  C
41, 3syl6req 2131 1  |-  ( ph  ->  C  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285
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 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-cleq 2075
This theorem is referenced by:  iftrue  3364  iffalse  3367  difprsn1  3533  dmmptg  4848  relcoi1  4879  funimacnv  5006  dffv3g  5205  dfimafn  5254  fvco2  5274  isoini  5488  oprabco  5869  unfiexmid  6438  undiffi  6443  supval2ti  6467  eqneg  7887  zeo  8533  fseq1p1m1  9187  iseqval  9530  iseqvalt  9532  mulgcd  10549  ialgrp1  10572  ialgcvg  10574
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