ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm5.18im Unicode version

Theorem pm5.18im 1367
Description: One direction of pm5.18dc 869, which holds for all propositions, not just decidable propositions. (Contributed by Jim Kingdon, 10-Mar-2018.)
Assertion
Ref Expression
pm5.18im  |-  ( (
ph 
<->  ps )  ->  -.  ( ph  <->  -.  ps )
)

Proof of Theorem pm5.18im
StepHypRef Expression
1 pm5.19 696 . 2  |-  -.  ( ps 
<->  -.  ps )
2 bibi1 239 . . 3  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  -.  ps )  <->  ( ps  <->  -.  ps )
) )
32notbid 657 . 2  |-  ( (
ph 
<->  ps )  ->  ( -.  ( ph  <->  -.  ps )  <->  -.  ( ps  <->  -.  ps )
) )
41, 3mpbiri 167 1  |-  ( (
ph 
<->  ps )  ->  -.  ( ph  <->  -.  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 104
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-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  xornbi  1368
  Copyright terms: Public domain W3C validator