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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  192  con34b  315  nic-ax  1667  nic-axALT  1668  axc10  2379  camestres  2663  baroco  2666  rexim  3083  falseral0  4521  nrhmzr  20479  dfon2lem9  35392  hbntg  35406  naim1  35878  naim2  35879  lukshef-ax2  35904  bj-eximALT  36122  bj-axc10v  36275  ax12indn  38419  cvrexchlem  38896  cvratlem  38898  axfrege28  43262  vk15.4j  43970  tratrb  43978  hbntal  43995  tratrbVD  44303  con5VD  44342  vk15.4jVD  44356
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