Theorem feq2d 5216

Description: Equality deduction for functions. (Contributed by Paul Chapman, 22-Jun-2011.)

Hypothesis

Ref	Expression
feq2d.1	|- (ph -> A = B)

Assertion

Ref	Expression
feq2d	|- (ph -> (F:A-->C <-> F:B-->C))

Proof of Theorem feq2d

Step	Hyp	Ref	Expression
1		feq2d.1	. 2 |- (ph -> A = B)
2		feq2 5212	. 2 |- (A = B -> (F:A-->C <-> F:B-->C))
3	1, 2	syl 15	1 |- (ph -> (F:A-->C <-> F:B-->C))

Syntax hints:   -> wi 4   <-> wb 176   = wceq 1642  -->wf 4778

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-an 360  df-ex 1542  df-cleq 2346  df-fn 4791  df-f 4792

This theorem is referenced by:  feq12d  5217  ffdm  5235  fsng  5434