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Theorem con3 134
Description: Contraposition. Theorem *2.16 of [WhiteheadRussell] p. 103. This was the fourth axiom of Frege, specifically Proposition 28 of [Frege1879] p. 43. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 13-Feb-2013.)
Assertion
Ref Expression
con3  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )

Proof of Theorem con3
StepHypRef Expression
1 id 22 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21con3d 133 1  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  pm2.65  172  con34b  292  nic-ax  1490  nic-axALT  1491  eximOLD  1634  axc10  1973  ax12indn  2266  rexim  2929  ralf0  3934  dfon2lem9  28800  hbntg  28815  naim1  29427  naim2  29428  lukshef-ax2  29457  vk15.4j  32377  tratrb  32386  hbntal  32406  tratrbVD  32741  con5VD  32780  vk15.4jVD  32794  bj-axc10v  33359  cvrexchlem  34215  cvratlem  34217  axfrege28  36840  bj-frege52a  36868
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