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)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  mt4i  119  pm2.18d  128  phpeqd  9228  fin1a2s  10493  gchinf  10743  pwfseqlem4  10748  pcfac  17078  prmreclem3  17097  sylow1lem1  19813  irredrmul  20658  mdetunilem9  22936  ioorcl2  25894  itg2gt0  26082  mdegmullem  26397  atom1d  32956  rr-phpd  45283  notnotrALT  45588  fourierdlem79  47271