Theorem fneq2i 5451

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 5445	. 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 105   = wceq 1398   Fn wfn 5347

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1496  ax-gen 1498  ax-4 1559  ax-17 1575  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-cleq 2225  df-fn 5355

This theorem is referenced by:  fnunsn  5465  tpos0  6505  dfixp  6935  xnn0nnen  10799  ser0f  10896  fnpr2o  13552  vtxedgfi  16284  vtxlpfi  16285