Theorem mt4d 117

Description: Modus tollens deduction. Deduction form of mt4 116. (Contributed by NM, 9-Jun-2006.)

Hypotheses

Ref	Expression
mt4d.1	⊢ (𝜑 → 𝜓)
mt4d.2	⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓))

Assertion

Ref	Expression
mt4d	⊢ (𝜑 → 𝜒)

Proof of Theorem mt4d

Step	Hyp	Ref	Expression
1		mt4d.1	. 2 ⊢ (𝜑 → 𝜓)
2		mt4d.2	. . 3 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓))
3	2	con4d 115	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	1, 3	mpd 15	1 ⊢ (𝜑 → 𝜒)

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  9137  fin1a2s  10325  gchinf  10569  pwfseqlem4  10574  pcfac  16859  prmreclem3  16878  sylow1lem1  19562  irredrmul  20396  mdetunilem9  22594  ioorcl2  25548  itg2gt0  25736  mdegmullem  26055  atom1d  32444  rr-phpd  44651  notnotrALT  44971  fourierdlem79  46628