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Theorem con2b 325
Description: Contraposition. Bidirectional version of con2 110. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con2b  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)

Proof of Theorem con2b
StepHypRef Expression
1 con2 110 . 2  |-  ( (
ph  ->  -.  ps )  ->  ( ps  ->  -.  ph ) )
2 con2 110 . 2  |-  ( ( ps  ->  -.  ph )  ->  ( ph  ->  -.  ps ) )
31, 2impbii 181 1  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177
This theorem is referenced by:  mt2bi  329  pm4.15  565  nic-ax  1447  nic-axALT  1448  ssconb  3472  disjsn  3860  oneqmini  4624  kmlem4  8025  isprm3  13080  pm13.196a  27582  bnj1171  29306  bnj1176  29311  bnj1204  29318  bnj1388  29339  bnj1523  29377
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178
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