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Theorem con2b 335
Description: Contraposition. Bidirectional version of con2 119. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
con2b  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)

Proof of Theorem con2b
StepHypRef Expression
1 con2 119 . 2  |-  ( (
ph  ->  -.  ps )  ->  ( ps  ->  -.  ph ) )
2 con2 119 . 2  |-  ( ( ps  ->  -.  ph )  ->  ( ph  ->  -.  ps ) )
31, 2impbii 190 1  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187
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 188
This theorem is referenced by:  mt2bi  339  pm4.15  583  nic-ax  1552  nic-axALT  1553  alimex  1699  ssconb  3604  disjsn  4063  oneqmini  5493  kmlem4  8581  isprm3  14604  bnj1171  29597  bnj1176  29602  bnj1204  29609  bnj1388  29630  bnj1523  29668  wl-nancom  31559  dfxor5  35998  pm13.196a  36402
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