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Theorem con1biimdc 801
Description: Contraposition. (Contributed by Jim Kingdon, 4-Apr-2018.)
Assertion
Ref Expression
con1biimdc  |-  (DECID  ph  ->  ( ( -.  ph  <->  ps )  ->  ( -.  ps  <->  ph ) ) )

Proof of Theorem con1biimdc
StepHypRef Expression
1 bi1 116 . . 3  |-  ( ( -.  ph  <->  ps )  ->  ( -.  ph  ->  ps )
)
2 con1dc 787 . . 3  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  ->  ( -.  ps  ->  ph ) ) )
31, 2syl5 32 . 2  |-  (DECID  ph  ->  ( ( -.  ph  <->  ps )  ->  ( -.  ps  ->  ph ) ) )
4 bi2 128 . . . 4  |-  ( ( -.  ph  <->  ps )  ->  ( ps  ->  -.  ph ) )
54con2d 587 . . 3  |-  ( ( -.  ph  <->  ps )  ->  ( ph  ->  -.  ps )
)
65a1i 9 . 2  |-  (DECID  ph  ->  ( ( -.  ph  <->  ps )  ->  ( ph  ->  -.  ps ) ) )
73, 6impbidd 125 1  |-  (DECID  ph  ->  ( ( -.  ph  <->  ps )  ->  ( -.  ps  <->  ph ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103  DECID wdc 776
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  ax-io 663
This theorem depends on definitions:  df-bi 115  df-dc 777
This theorem is referenced by:  con1bidc  802  con1biddc  804
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