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Theorem con3 631
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 620 1  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 603  ax-in2 604
This theorem is referenced by:  mtt  674  annimim  675  pm3.37  678  const  837  con34bdc  856  hbnt  1631  ralf0  3466  ltleletr  7853  ltnsym  7857  bj-nnsn  12975  bj-nnclavius  12980
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