Theorem mt4d 152

Description: Modus tollens deduction. Deduction form of mt4 115. (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 114	. 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  153  fin1a2s  9428  gchinf  9671  pwfseqlem4  9676  pcfac  15805  prmreclem3  15824  sylow1lem1  18213  irredrmul  18907  mdetunilem9  20628  ioorcl2  23540  itg2gt0  23726  mdegmullem  24037  atom1d  29521  notnotrALT  39237  fourierdlem79  40905