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Theorem pm5.18im 1321
Description: One direction of pm5.18dc 815, 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 pm5.19 657 . 2  |-  -.  ( ps 
<->  -.  ps )
2 bibi1 238 . . 3  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  -.  ps )  <->  ( ps  <->  -.  ps )
) )
32notbid 627 . 2  |-  ( (
ph 
<->  ps )  ->  ( -.  ( ph  <->  -.  ps )  <->  -.  ( ps  <->  -.  ps )
) )
41, 3mpbiri 166 1  |-  ( (
ph 
<->  ps )  ->  -.  ( ph  <->  -.  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> 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  ax-in1 579  ax-in2 580
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  xornbi  1322
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