Theorem fneq2i 5180

Description: Equality inference for function predicate with domain. (Contributed by set.mm contributors, 4-Sep-2011.)

Hypothesis

Ref	Expression
fneq2i.1	⊢ A = B

Assertion

Ref	Expression
fneq2i	⊢ (F Fn A ↔ F Fn B)

Proof of Theorem fneq2i

Step	Hyp	Ref	Expression
1		fneq2i.1	. 2 ⊢ A = B
2		fneq2 5175	. 2 ⊢ (A = B → (F Fn A ↔ F Fn B))
3	1, 2	ax-mp 5	1 ⊢ (F Fn A ↔ F Fn B)

Syntax hints:   ↔ wb 176   = wceq 1642   Fn wfn 4777

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

This theorem is referenced by:  fnunsn  5191  ovg  5602  fncup  5814  addcfn  5826  fncross  5847  fnmap  6008  fnpm  6009  xpassen  6058  fnce  6177