ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  a1bi Unicode version

Theorem a1bi 241
Description: Inference rule introducing a theorem as an antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 11-Nov-2012.)
Hypothesis
Ref Expression
a1bi.1  |-  ph
Assertion
Ref Expression
a1bi  |-  ( ps  <->  (
ph  ->  ps ) )

Proof of Theorem a1bi
StepHypRef Expression
1 a1bi.1 . 2  |-  ph
2 biimt 239 . 2  |-  ( ph  ->  ( ps  <->  ( ph  ->  ps ) ) )
31, 2ax-mp 7 1  |-  ( ps  <->  (
ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  mt2bi  642  truimfal  1342  equsal  1657  equveli  1684  ralv  2627  relop  4544
  Copyright terms: Public domain W3C validator