Theorem syl6reqr 2404

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

Hypotheses

Ref	Expression
syl6reqr.1	⊢ (φ → A = B)
syl6reqr.2	⊢ C = B

Assertion

Ref	Expression
syl6reqr	⊢ (φ → C = A)

Proof of Theorem syl6reqr

Step	Hyp	Ref	Expression
1		syl6reqr.1	. 2 ⊢ (φ → A = B)
2		syl6reqr.2	. . 3 ⊢ C = B
3	2	eqcomi 2357	. 2 ⊢ B = C
4	1, 3	syl6req 2402	1 ⊢ (φ → C = A)

Syntax hints:   → wi 4   = wceq 1642

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  iftrue  3668  iffalse  3669  difprsn1  3847  funimacnv  5168  dfimafn  5366  fniinfv  5372  fvco2  5382  fniunfv  5466  isoini  5497  dmmptg  5684  nchoicelem14  6302