Theorem fneq1d 5364

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

Hypothesis

Ref	Expression
fneq1d.1	|- ( ph -> F = G )

Assertion

Ref	Expression
fneq1d	|- ( ph -> ( F Fn A <-> G Fn A ) )

Proof of Theorem fneq1d

Step	Hyp	Ref	Expression
1		fneq1d.1	. 2 |- ( ph -> F = G )
2		fneq1 5362	. 2 |- ( F = G -> ( F Fn A <-> G Fn A ) )
3	1, 2	syl 14	1 |- ( ph -> ( F Fn A <-> G Fn A ) )

Syntax hints:   -> wi 4   <-> wb 105   = wceq 1373   Fn wfn 5266

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-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-un 3170  df-in 3172  df-ss 3179  df-sn 3639  df-pr 3640  df-op 3642  df-br 4045  df-opab 4106  df-rel 4682  df-cnv 4683  df-co 4684  df-dm 4685  df-fun 5273  df-fn 5274

This theorem is referenced by:  fneq12d  5366  f1o00  5557  f1ompt  5731  fmpt2d  5742  f1ocnvd  6148  offval2  6174  ofrfval2  6175  caofinvl  6184  f1od2  6321  cc3  7380  ccatvalfn  11057  swrdlen  11105  plusffng  13197  grpinvfng  13376  grpinvf1o  13402  mulgfng  13460  srg1zr  13749  scaffng  14071  neif  14613  fnmptd  15740