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Theorem con2b 332
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  336  pm4.15  579  nic-ax  1510  nic-axALT  1511  alimex  1657  ssconb  3623  disjsn  4076  oneqmini  4918  kmlem4  8524  isprm3  14310  wl-nancom  30212  pm13.196a  31562  bnj1171  34457  bnj1176  34462  bnj1204  34469  bnj1388  34490  bnj1523  34528  dfxor5  38240
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