ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  feq1i Unicode version

Theorem feq1i 5039
Description: Equality inference for functions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
feq1i.1  |-  F  =  G
Assertion
Ref Expression
feq1i  |-  ( F : A --> B  <->  G : A
--> B )

Proof of Theorem feq1i
StepHypRef Expression
1 feq1i.1 . 2  |-  F  =  G
2 feq1 5030 . 2  |-  ( F  =  G  ->  ( F : A --> B  <->  G : A
--> B ) )
31, 2ax-mp 7 1  |-  ( F : A --> B  <->  G : A
--> B )
Colors of variables: wff set class
Syntax hints:    <-> wb 98    = wceq 1243   -->wf 4898
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-rel 4352  df-cnv 4353  df-co 4354  df-dm 4355  df-rn 4356  df-fun 4904  df-fn 4905  df-f 4906
This theorem is referenced by:  ftpg  5347  resqrexlemf  9605  ialgrf  9884
  Copyright terms: Public domain W3C validator