Theorem syl6reqr 2091

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

Step	Hyp	Ref	Expression
1		syl6reqr.1	. 2 |- ( ph -> A = B )
2		syl6reqr.2	. . 3 |- C = B
3	2	eqcomi 2044	. 2 |- B = C
4	1, 3	syl6req 2089	1 |- ( ph -> C = A )

Syntax hints:   -> wi 4   = wceq 1243

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 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033

This theorem is referenced by:  iftrue  3336  iffalse  3339  difprsn1  3503  dmmptg  4818  relcoi1  4849  funimacnv  4975  dffv3g  5174  dfimafn  5222  fvco2  5242  isoini  5457  oprabco  5838  eqneg  7708  zeo  8343  fseq1p1m1  8956  iseqval  9220  ialgrp1  9885  ialgcvg  9887