Theorem fneq1d 5363

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 5361	. 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 1372   Fn wfn 5265

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 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-v 2773  df-un 3169  df-in 3171  df-ss 3178  df-sn 3638  df-pr 3639  df-op 3641  df-br 4044  df-opab 4105  df-rel 4681  df-cnv 4682  df-co 4683  df-dm 4684  df-fun 5272  df-fn 5273

This theorem is referenced by:  fneq12d  5365  f1o00  5556  f1ompt  5730  fmpt2d  5741  f1ocnvd  6147  offval2  6173  ofrfval2  6174  caofinvl  6183  f1od2  6320  cc3  7379  ccatvalfn  11055  plusffng  13168  grpinvfng  13347  grpinvf1o  13373  mulgfng  13431  srg1zr  13720  scaffng  14042  neif  14584  fnmptd  15702