Theorem fneq2d 5421

Description: Equality deduction for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)

Hypothesis

Ref	Expression
fneq2d.1	|- ( ph -> A = B )

Assertion

Ref	Expression
fneq2d	|- ( ph -> ( F Fn A <-> F Fn B ) )

Proof of Theorem fneq2d

Step	Hyp	Ref	Expression
1		fneq2d.1	. 2 |- ( ph -> A = B )
2		fneq2 5419	. 2 |- ( A = B -> ( F Fn A <-> F Fn B ) )
3	1, 2	syl 14	1 |- ( ph -> ( F Fn A <-> F Fn B ) )

Syntax hints:   -> wi 4   <-> wb 105   = wceq 1397   Fn wfn 5321

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 1495  ax-gen 1497  ax-4 1558  ax-17 1574  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-fn 5329

This theorem is referenced by:  fneq12d  5422  fncofn  5831  acfun  7421  ccfunen  7482  ccatlid  11182  ccatrid  11183  ccatass  11184  ccatswrd  11250  swrdccat2  11251  ccatpfx  11281  swrdswrd  11285  swrdccatin2  11309  pfxccatin12  11313  seq3shft  11398  ptex  13346  srg1zr  13999