Theorem syl5req 2127

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 2126	. 2 |- ( ph -> A = C )
4	3	eqcomd 2087	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:  syl5reqr  2129  opeqsn  4015  relop  4514  funopg  4964  funcnvres  5003  apreap  7754  recextlem1  7808  nn0supp  8407  intqfrac2  9401  sizeprg  9832