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Theorem con2b 628
Description: Contraposition. Bidirectional version of con2 607. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con2b  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)

Proof of Theorem con2b
StepHypRef Expression
1 con2 607 . 2  |-  ( (
ph  ->  -.  ps )  ->  ( ps  ->  -.  ph ) )
2 con2 607 . 2  |-  ( ( ps  ->  -.  ph )  ->  ( ph  ->  -.  ps ) )
31, 2impbii 124 1  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  mt2bi  644  pm4.15  827  dfdif3  3108  ssconb  3131  disjsn  3499  isprm3  11193
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