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

Theorem iotabii 5002
Description: Formula-building deduction for iota. (Contributed by Mario Carneiro, 2-Oct-2015.)
Hypothesis
Ref Expression
iotabii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
iotabii  |-  ( iota
x ph )  =  ( iota x ps )

Proof of Theorem iotabii
StepHypRef Expression
1 iotabi 4989 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( iota x ph )  =  ( iota x ps ) )
2 iotabii.1 . 2  |-  ( ph  <->  ps )
31, 2mpg 1385 1  |-  ( iota
x ph )  =  ( iota x ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1289   iotacio 4978
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-uni 3654  df-iota 4980
This theorem is referenced by:  riotav  5613  cbvsum  10749
  Copyright terms: Public domain W3C validator