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Theorem con3 604
Description: Contraposition. Theorem *2.16 of [WhiteheadRussell] p. 103. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 13-Feb-2013.)
Assertion
Ref Expression
con3  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )

Proof of Theorem con3
StepHypRef Expression
1 id 19 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21con3d 594 1  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 577  ax-in2 578
This theorem is referenced by:  mtt  643  con34bdc  801  annimim  818  pm3.37  824  hbnt  1586  ralf0  3372  ltleletr  7511  ltnsym  7515
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