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Theorem con1biddc 806
Description: A contraposition deduction. (Contributed by Jim Kingdon, 4-Apr-2018.)
Hypothesis
Ref Expression
con1biddc.1  |-  ( ph  ->  (DECID  ps  ->  ( -.  ps 
<->  ch ) ) )
Assertion
Ref Expression
con1biddc  |-  ( ph  ->  (DECID  ps  ->  ( -.  ch 
<->  ps ) ) )

Proof of Theorem con1biddc
StepHypRef Expression
1 con1biddc.1 . 2  |-  ( ph  ->  (DECID  ps  ->  ( -.  ps 
<->  ch ) ) )
2 con1biimdc 803 . 2  |-  (DECID  ps  ->  ( ( -.  ps  <->  ch )  ->  ( -.  ch  <->  ps )
) )
31, 2sylcom 28 1  |-  ( ph  ->  (DECID  ps  ->  ( -.  ch 
<->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103  DECID wdc 778
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 779
This theorem is referenced by:  con2biddc  810  pm5.18dc  813  necon1abiddc  2313  necon1bbiddc  2314
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