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Theorem con2biddc 808
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 138 . . . 4  |-  ( ( ps  <->  -.  ch )  <->  ( -.  ch  <->  ps )
)
31, 2syl6ib 159 . . 3  |-  ( ph  ->  (DECID  ch  ->  ( -.  ch 
<->  ps ) ) )
43con1biddc 804 . 2  |-  ( ph  ->  (DECID  ch  ->  ( -.  ps 
<->  ch ) ) )
5 bicom 138 . 2  |-  ( ( -.  ps  <->  ch )  <->  ( ch  <->  -.  ps )
)
64, 5syl6ib 159 1  |-  ( ph  ->  (DECID  ch  ->  ( ch  <->  -. 
ps ) ) )
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:  anordc  898  xor3dc  1319
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