Theorem fneq1d 5208

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 5206	. 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 104   = wceq 1331   Fn wfn 5113

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-opab 3985  df-rel 4541  df-cnv 4542  df-co 4543  df-dm 4544  df-fun 5120  df-fn 5121

This theorem is referenced by:  fneq12d  5210  f1o00  5395  f1ompt  5564  fmpt2d  5575  f1ocnvd  5965  offval2  5990  ofrfval2  5991  caofinvl  5997  f1od2  6125  neif  12299