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  9169  fin1a2s  10361  gchinf  10605  pwfseqlem4  10610  pcfac  16911  prmreclem3  16930  sylow1lem1  19614  irredrmul  20448  mdetunilem9  22653  ioorcl2  25607  itg2gt0  25795  mdegmullem  26111  atom1d  32495  rr-phpd  44733  notnotrALT  45053  fourierdlem79  46707