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Theorem con2b 340
Description: Contraposition. Bidirectional version of con2 121. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
con2b  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)

Proof of Theorem con2b
StepHypRef Expression
1 con2 121 . 2  |-  ( (
ph  ->  -.  ps )  ->  ( ps  ->  -.  ph ) )
2 con2 121 . 2  |-  ( ( ps  ->  -.  ph )  ->  ( ph  ->  -.  ps ) )
31, 2impbii 192 1  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 189
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 190
This theorem is referenced by:  mt2bi  344  pm4.15  589  nic-ax  1560  nic-axALT  1561  alimex  1707  ssconb  3534  disjsn  4000  oneqmini  5453  kmlem4  8570  isprm3  14644  bnj1171  29815  bnj1176  29820  bnj1204  29827  bnj1388  29848  bnj1523  29886  wl-nancom  31854  dfxor5  36361  pm13.196a  36766
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