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Theorem con1biimdc 859
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 biimp 117 . . 3  |-  ( ( -.  ph  <->  ps )  ->  ( -.  ph  ->  ps )
)
2 con1dc 842 . . 3  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  ->  ( -.  ps  ->  ph ) ) )
31, 2syl5 32 . 2  |-  (DECID  ph  ->  ( ( -.  ph  <->  ps )  ->  ( -.  ps  ->  ph ) ) )
4 biimpr 129 . . . 4  |-  ( ( -.  ph  <->  ps )  ->  ( ps  ->  -.  ph ) )
54con2d 614 . . 3  |-  ( ( -.  ph  <->  ps )  ->  ( ph  ->  -.  ps )
)
65a1i 9 . 2  |-  (DECID  ph  ->  ( ( -.  ph  <->  ps )  ->  ( ph  ->  -.  ps ) ) )
73, 6impbidd 126 1  |-  (DECID  ph  ->  ( ( -.  ph  <->  ps )  ->  ( -.  ps  <->  ph ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 104  DECID wdc 820
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  ax-io 699
This theorem depends on definitions:  df-bi 116  df-stab 817  df-dc 821
This theorem is referenced by:  con1bidc  860  con1biddc  862
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