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Theorem con3 153
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 154. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 13-Feb-2013.)
Assertion
Ref Expression
con3 ((𝜑𝜓) → (¬ 𝜓 → ¬ 𝜑))

Proof of Theorem con3
StepHypRef Expression
1 id 22 . 2 ((𝜑𝜓) → (𝜑𝜓))
21con3d 152 1 ((𝜑𝜓) → (¬ 𝜓 → ¬ 𝜑))
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  193  con34b  316  nic-ax  1670  nic-axALT  1671  axc10  2388  camestres  2671  baroco  2674  rexim  3085  falseral0  4522  nrhmzr  20554  cbvex1v  35067  dfon2lem9  35773  hbntg  35787  naim1  36372  naim2  36373  lukshef-ax2  36398  bj-eximALT  36624  bj-axc10v  36776  ax12indn  38925  cvrexchlem  39402  cvratlem  39404  axfrege28  43819  vk15.4j  44526  tratrb  44534  hbntal  44551  tratrbVD  44859  con5VD  44898  vk15.4jVD  44912
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