Theorem fneq2i 5143

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 5137	. 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 104   = wceq 1296   Fn wfn 5044

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-4 1452  ax-17 1471  ax-ext 2077

This theorem depends on definitions:  df-bi 116  df-cleq 2088  df-fn 5052

This theorem is referenced by:  fnunsn  5155  tpos0  6077  dfixp  6497  ser0f  10081