Theorem fneq1d 5345

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 5343	. 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 1364   Fn wfn 5250

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3158  df-in 3160  df-ss 3167  df-sn 3625  df-pr 3626  df-op 3628  df-br 4031  df-opab 4092  df-rel 4667  df-cnv 4668  df-co 4669  df-dm 4670  df-fun 5257  df-fn 5258

This theorem is referenced by:  fneq12d  5347  f1o00  5536  f1ompt  5710  fmpt2d  5721  f1ocnvd  6122  offval2  6148  ofrfval2  6149  caofinvl  6157  f1od2  6290  cc3  7330  plusffng  12951  grpinvfng  13119  grpinvf1o  13145  mulgfng  13197  srg1zr  13486  scaffng  13808  neif  14320  fnmptd  15366