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Theorem con1biidc 805
Description: A contraposition inference. (Contributed by Jim Kingdon, 15-Mar-2018.)
Hypothesis
Ref Expression
con1biidc.1  |-  (DECID  ph  ->  ( -.  ph  <->  ps ) )
Assertion
Ref Expression
con1biidc  |-  (DECID  ph  ->  ( -.  ps  <->  ph ) )

Proof of Theorem con1biidc
StepHypRef Expression
1 notnotbdc 800 . . 3  |-  (DECID  ph  ->  (
ph 
<->  -.  -.  ph )
)
2 con1biidc.1 . . . 4  |-  (DECID  ph  ->  ( -.  ph  <->  ps ) )
32notbid 625 . . 3  |-  (DECID  ph  ->  ( -.  -.  ph  <->  -.  ps )
)
41, 3bitrd 186 . 2  |-  (DECID  ph  ->  (
ph 
<->  -.  ps ) )
54bicomd 139 1  |-  (DECID  ph  ->  ( -.  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:  con2biidc  807  necon1abiidc  2309  necon1bbiidc  2310
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