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Theorem con2b 334
Description: Contraposition. Bidirectional version of con2 116. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
con2b  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)

Proof of Theorem con2b
StepHypRef Expression
1 con2 116 . 2  |-  ( (
ph  ->  -.  ps )  ->  ( ps  ->  -.  ph ) )
2 con2 116 . 2  |-  ( ( ps  ->  -.  ph )  ->  ( ph  ->  -.  ps ) )
31, 2impbii 188 1  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185
This theorem is referenced by:  mt2bi  338  pm4.15  581  nic-ax  1481  nic-axALT  1482  ssconb  3590  disjsn  4037  oneqmini  4871  kmlem4  8426  isprm3  13883  pm13.196a  29809  bnj1171  32294  bnj1176  32299  bnj1204  32306  bnj1388  32327  bnj1523  32365  bj-alimex  32452
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