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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  9215  phpeqdOLD  9225  fin1a2s  10409  gchinf  10652  pwfseqlem4  10657  pcfac  16832  prmreclem3  16851  sylow1lem1  19466  irredrmul  20241  mdetunilem9  22122  ioorcl2  25089  itg2gt0  25278  mdegmullem  25596  atom1d  31606  rr-phpd  42962  notnotrALT  43290  fourierdlem79  44901
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