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

Theorem imorri 744
Description: Infer implication from disjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypothesis
Ref Expression
imorri.1  |-  ( -. 
ph  \/  ps )
Assertion
Ref Expression
imorri  |-  ( ph  ->  ps )

Proof of Theorem imorri
StepHypRef Expression
1 imorri.1 . 2  |-  ( -. 
ph  \/  ps )
2 pm2.21 612 . . 3  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
3 ax-1 6 . . 3  |-  ( ps 
->  ( ph  ->  ps ) )
42, 3jaoi 711 . 2  |-  ( ( -.  ph  \/  ps )  ->  ( ph  ->  ps ) )
51, 4ax-mp 5 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 703
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 610  ax-io 704
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator