ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  feq1d Unicode version

Theorem feq1d 5065
Description: Equality deduction for functions. (Contributed by NM, 19-Feb-2008.)
Hypothesis
Ref Expression
feq1d.1  |-  ( ph  ->  F  =  G )
Assertion
Ref Expression
feq1d  |-  ( ph  ->  ( F : A --> B 
<->  G : A --> B ) )

Proof of Theorem feq1d
StepHypRef Expression
1 feq1d.1 . 2  |-  ( ph  ->  F  =  G )
2 feq1 5061 . 2  |-  ( F  =  G  ->  ( F : A --> B  <->  G : A
--> B ) )
31, 2syl 14 1  |-  ( ph  ->  ( F : A --> B 
<->  G : A --> B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    = wceq 1285   -->wf 4928
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-rel 4378  df-cnv 4379  df-co 4380  df-dm 4381  df-rn 4382  df-fun 4934  df-fn 4935  df-f 4936
This theorem is referenced by:  feq12d  5067  fco2  5088  fssres2  5098  fresin  5099  fmptco  5362  fressnfv  5382  off  5755  caofinvl  5764  f2ndf  5878  eroprf  6265  fseq1p1m1  9187  climserile  10321
  Copyright terms: Public domain W3C validator