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Theorem con2biddc 774
Description: A contraposition deduction. (Contributed by Jim Kingdon, 11-Apr-2018.)
Hypothesis
Ref Expression
con2biddc.1  |-  ( ph  ->  (DECID  ch  ->  ( ps  <->  -. 
ch ) ) )
Assertion
Ref Expression
con2biddc  |-  ( ph  ->  (DECID  ch  ->  ( ch  <->  -. 
ps ) ) )

Proof of Theorem con2biddc
StepHypRef Expression
1 con2biddc.1 . . . 4  |-  ( ph  ->  (DECID  ch  ->  ( ps  <->  -. 
ch ) ) )
2 bicom 128 . . . 4  |-  ( ( ps  <->  -.  ch )  <->  ( -.  ch  <->  ps )
)
31, 2syl6ib 150 . . 3  |-  ( ph  ->  (DECID  ch  ->  ( -.  ch 
<->  ps ) ) )
43con1biddc 770 . 2  |-  ( ph  ->  (DECID  ch  ->  ( -.  ps 
<->  ch ) ) )
5 bicom 128 . 2  |-  ( ( -.  ps  <->  ch )  <->  ( ch  <->  -.  ps )
)
64, 5syl6ib 150 1  |-  ( ph  ->  (DECID  ch  ->  ( ch  <->  -. 
ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 98  DECID wdc 742
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630
This theorem depends on definitions:  df-bi 110  df-dc 743
This theorem is referenced by:  anordc  863  xor3dc  1278
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