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Theorem con3 149
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 150. (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 148 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  306  nic-ax  1595  nic-axALT  1596  axc10  2251  rexim  3004  ralf0OLD  4057  falseral0  4059  dfon2lem9  31450  hbntg  31465  naim1  32079  naim2  32080  lukshef-ax2  32109  bj-axc10v  32412  ax12indn  33747  cvrexchlem  34224  cvratlem  34226  axfrege28  37644  vk15.4j  38255  tratrb  38267  hbntal  38290  tratrbVD  38619  con5VD  38658  vk15.4jVD  38672  nrhmzr  41191
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