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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  8694  fin1a2s  9829  gchinf  10072  pwfseqlem4  10077  pcfac  16228  prmreclem3  16247  sylow1lem1  18718  irredrmul  19456  mdetunilem9  21228  ioorcl2  24179  itg2gt0  24367  mdegmullem  24682  atom1d  30139  rr-phpd  40903  notnotrALT  41222  fourierdlem79  42814
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