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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  290  nic-ax  1510  nic-axALT  1511  eximOLD  1660  axc10  2009  ax12indn  2275  rexim  2919  ralf0  3924  dfon2lem9  29466  hbntg  29481  naim1  30081  naim2  30082  lukshef-ax2  30111  nrhmzr  32952  vk15.4j  33704  tratrb  33716  hbntal  33739  tratrbVD  34081  con5VD  34120  vk15.4jVD  34134  bj-axc10v  34697  cvrexchlem  35559  cvratlem  35561  axfrege28  38330
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