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Theorem con2 110
Description: Contraposition. Theorem *2.03 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Feb-2013.)
Assertion
Ref Expression
con2  |-  ( (
ph  ->  -.  ps )  ->  ( ps  ->  -.  ph ) )

Proof of Theorem con2
StepHypRef Expression
1 id 21 . 2  |-  ( (
ph  ->  -.  ps )  ->  ( ph  ->  -.  ps ) )
21con2d 109 1  |-  ( (
ph  ->  -.  ps )  ->  ( ps  ->  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6
This theorem is referenced by:  con2b  326  ax12o10lem3  1637  ax4  1691  isprm5  12665  ax9lem3  27831
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
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