Theorem syl5reqr 2129

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 2086	. 2 |- A = B
3		syl5reqr.2	. 2 |- ( ph -> B = C )
4	2, 3	syl5req 2127	1 |- ( ph -> C = A )

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:  bm2.5ii  4242  resdmdfsn  4675  f1o00  5186  fmpt  5345  fmptsn  5378  resfunexg  5408  pm54.43  6508  prarloclem5  6741  recexprlem1ssl  6874  recexprlem1ssu  6875  iooval2  9003  sizesng  9811  resqrexlemover  10023