Theorem syl5req 2082

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

Hypotheses

Ref	Expression
syl5req.1	|- A = B
syl5req.2	|- (ph -> B = C)

Assertion

Ref	Expression
syl5req	|- (ph -> C = A)

Proof of Theorem syl5req

Step	Hyp	Ref	Expression
1		syl5req.1	. . 3 |- A = B
2		syl5req.2	. . 3 |- (ph -> B = C)
3	1, 2	syl5eq 2081	. 2 |- (ph -> A = C)
4	3	eqcomd 2042	1 |- (ph -> C = A)

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:  syl5reqr  2084  opeqsn  3980  relop  4429  funopg  4877  funcnvres  4915  apreap  7371  recextlem1  7414  nn0supp  8010