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  9116  fin1a2s  10297  gchinf  10540  pwfseqlem4  10545  pcfac  16803  prmreclem3  16822  sylow1lem1  19503  irredrmul  20338  mdetunilem9  22528  ioorcl2  25493  itg2gt0  25681  mdegmullem  26003  atom1d  32323  rr-phpd  44221  notnotrALT  44541  fourierdlem79  46202