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Theorem con3 139
Description: Contraposition. Theorem *2.16 of [WhiteheadRussell] p. 103. This was the fourth axiom of Frege, specifically Proposition 28 of [Frege1879] p. 43. Its associated inference is con3i 140. (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 23 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21con3d 138 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  175  con34b  293  nic-ax  1552  nic-axALT  1553  axc10  2058  rexim  2890  ralf0  3904  dfon2lem9  30432  hbntg  30447  naim1  31038  naim2  31039  lukshef-ax2  31068  bj-axc10v  31265  ax12indn  32433  cvrexchlem  32903  cvratlem  32905  axfrege28  36283  vk15.4j  36743  tratrb  36755  hbntal  36778  tratrbVD  37119  con5VD  37158  vk15.4jVD  37172  nrhmzr  39145
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