Theorem fneq2i 5062

Description: Equality inference for function predicate with domain. (Contributed by NM, 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 5056	. 2 |- ( A = B -> ( F Fn A <-> F Fn B ) )
3	1, 2	ax-mp 7	1 |- ( F Fn A <-> F Fn B )

Syntax hints:   <-> wb 103   = wceq 1285   Fn wfn 4964

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 2065

This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-fn 4972

This theorem is referenced by:  fnunsn  5074  tpos0  5971  iser0f  9788