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Theorem pm5.18im 1396
Description: One direction of pm5.18dc 884, 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 pm5.19 707 . 2  |-  -.  ( ps 
<->  -.  ps )
2 bibi1 240 . . 3  |-  ( (
ph 
<->  ps )  ->  (
( ph  <->  -.  ps )  <->  ( ps  <->  -.  ps )
) )
32notbid 668 . 2  |-  ( (
ph 
<->  ps )  ->  ( -.  ( ph  <->  -.  ps )  <->  -.  ( ps  <->  -.  ps )
) )
41, 3mpbiri 168 1  |-  ( (
ph 
<->  ps )  ->  -.  ( ph  <->  -.  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  xornbi  1397
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