Theorem mt4d 130

Description: Modus tollens deduction. (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 97	. 2 ⊢ (φ → (ψ → χ))
4	1, 3	mpd 14	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  131