Theorem mt4d

Description: Modus tollens deduction. Deduction form of mt4 . (Contributed by NM, 9-Jun-2006)

	Ref	Expression
Hypotheses	mt4d.1	⊢ ( 𝜑 → 𝜓 )
	mt4d.2	⊢ ( 𝜑 → ( ¬ 𝜒 → ¬ 𝜓 ) )
Assertion	mt4d	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		mt4d.1	⊢ ( 𝜑 → 𝜓 )
2		mt4d.2	⊢ ( 𝜑 → ( ¬ 𝜒 → ¬ 𝜓 ) )
3	2	con4d	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	1 3	mpd	⊢ ( 𝜑 → 𝜒 )