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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  9166  phpeqdOLD  9176  fin1a2s  10359  gchinf  10602  pwfseqlem4  10607  pcfac  16782  prmreclem3  16801  sylow1lem1  19394  irredrmul  20152  mdetunilem9  22006  ioorcl2  24973  itg2gt0  25162  mdegmullem  25480  atom1d  31358  rr-phpd  42605  notnotrALT  42933  fourierdlem79  44546
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