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

Theorem feq1i 5373
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 5363 . 2  |-  ( F  =  G  ->  ( F : A --> B  <->  G : A
--> B ) )
31, 2ax-mp 5 1  |-  ( F : A --> B  <->  G : A
--> B )
Colors of variables: wff set class
Syntax hints:    <-> wb 105    = wceq 1364   -->wf 5227
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 2171
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3613  df-pr 3614  df-op 3616  df-br 4019  df-opab 4080  df-rel 4648  df-cnv 4649  df-co 4650  df-dm 4651  df-rn 4652  df-fun 5233  df-fn 5234  df-f 5235
This theorem is referenced by:  ftpg  5716  frecfcllem  6423  frecsuclem  6425  omp1eomlem  7111  frecuzrdgrcl  10428  frecuzrdgrclt  10433  fxnn0nninf  10456  resqrexlemf  11034  algrf  12063  eulerthlemh  12249  eulerthlemth  12250  ennnfonelemh  12423  nninfdclemf  12468  mulgval  13030  limcmpted  14529  dvexp  14572  efcn  14586  subctctexmid  15148
  Copyright terms: Public domain W3C validator