Theorem mt4d 118

Description: Modus tollens deduction. Deduction form of mt4 117. (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 116	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	1, 3	mpd 16	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  119  pm2.18d  128  phpeqd  9184  fin1a2s  10386  gchinf  10630  pwfseqlem4  10635  pcfac  16949  prmreclem3  16968  sylow1lem1  19659  irredrmul  20500  mdetunilem9  22738  ioorcl2  25692  itg2gt0  25880  mdegmullem  26196  atom1d  32614  rr-phpd  44797  notnotrALT  45103  fourierdlem79  46757