Theorem syl5reqr 2400

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

Hypotheses

Ref	Expression
syl5reqr.1	⊢ B = A
syl5reqr.2	⊢ (φ → B = C)

Assertion

Ref	Expression
syl5reqr	⊢ (φ → C = A)

Proof of Theorem syl5reqr

Step	Hyp	Ref	Expression
1		syl5reqr.1	. . 3 ⊢ B = A
2	1	eqcomi 2357	. 2 ⊢ A = B
3		syl5reqr.2	. 2 ⊢ (φ → B = C)
4	2, 3	syl5req 2398	1 ⊢ (φ → C = A)

Syntax hints:   → wi 4   = wceq 1642

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346

This theorem is referenced by:  vfin1cltv  4548  foima  5275  f1imacnv  5303  f1o00  5318  fmpt  5693  enmap1lem3  6072  dflec2  6211