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Theorem con3 150
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 151. (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 149 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  184  con34b  307  nic-ax  1753  nic-axALT  1754  axc10  2428  camestres  2749  baroco  2753  rexim  3206  falseral0  4285  dfon2lem9  32037  hbntg  32052  naim1  32726  naim2  32727  lukshef-ax2  32752  bj-axc10v  33053  ax12indn  34740  cvrexchlem  35217  cvratlem  35219  axfrege28  38640  vk15.4j  39249  tratrb  39261  hbntal  39284  tratrbVD  39608  con5VD  39647  vk15.4jVD  39661  nrhmzr  42458
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