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Theorem pm5.16 771
Description: Theorem *5.16 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm5.16  |-  -.  (
( ph  <->  ps )  /\  ( ph 
<->  -.  ps ) )

Proof of Theorem pm5.16
StepHypRef Expression
1 pm5.19 655 . 2  |-  -.  ( ps 
<->  -.  ps )
2 simpl 107 . . 3  |-  ( ( ( ph  <->  ps )  /\  ( ph  <->  -.  ps )
)  ->  ( ph  <->  ps ) )
3 simpr 108 . . 3  |-  ( ( ( ph  <->  ps )  /\  ( ph  <->  -.  ps )
)  ->  ( ph  <->  -. 
ps ) )
42, 3bitr3d 188 . 2  |-  ( ( ( ph  <->  ps )  /\  ( ph  <->  -.  ps )
)  ->  ( ps  <->  -. 
ps ) )
51, 4mto 621 1  |-  -.  (
( ph  <->  ps )  /\  ( ph 
<->  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 102    <-> 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 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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