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Theorem mt4d 117
Description: Modus tollens deduction. Deduction form of mt4 116. (Contributed by NM, 9-Jun-2006.)
Hypotheses
Ref Expression
mt4d.1 (𝜑𝜓)
mt4d.2 (𝜑 → (¬ 𝜒 → ¬ 𝜓))
Assertion
Ref Expression
mt4d (𝜑𝜒)

Proof of Theorem mt4d
StepHypRef Expression
1 mt4d.1 . 2 (𝜑𝜓)
2 mt4d.2 . . 3 (𝜑 → (¬ 𝜒 → ¬ 𝜓))
32con4d 115 . 2 (𝜑 → (𝜓𝜒))
41, 3mpd 15 1 (𝜑𝜒)
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:  mt4i  118  pm2.18d  127  phpeqd  9250  phpeqdOLD  9260  fin1a2s  10452  gchinf  10695  pwfseqlem4  10700  pcfac  16933  prmreclem3  16952  sylow1lem1  19631  irredrmul  20444  mdetunilem9  22642  ioorcl2  25621  itg2gt0  25810  mdegmullem  26132  atom1d  32382  rr-phpd  44199  notnotrALT  44527  fourierdlem79  46141
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