Theorem syl5req 2085

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 2084	. 2 |- ( ph -> A = C )
4	3	eqcomd 2045	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:  syl5reqr  2087  opeqsn  3989  relop  4486  funopg  4934  funcnvres  4972  apreap  7578  recextlem1  7632  nn0supp  8234  intqfrac2  9161