Theorem syl5reqr 2087

Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.)

Hypotheses

Ref	Expression
syl5reqr.1	|- B = A
syl5reqr.2	|- ( ph -> B = C )

Assertion

Ref	Expression
syl5reqr	|- ( ph -> C = A )

Proof of Theorem syl5reqr

Step	Hyp	Ref	Expression
1		syl5reqr.1	. . 3 |- B = A
2	1	eqcomi 2044	. 2 |- A = B
3		syl5reqr.2	. 2 |- ( ph -> B = C )
4	2, 3	syl5req 2085	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:  bm2.5ii  4222  f1o00  5161  fmpt  5319  fmptsn  5352  resfunexg  5382  prarloclem5  6598  recexprlem1ssl  6731  recexprlem1ssu  6732  iooval2  8784  resqrexlemover  9608