Theorem mt3d

Description: Modus tollens deduction. (Contributed by NM, 26-Mar-1995)

	Ref	Expression
Hypotheses	mt3d.1	⊢ ( 𝜑 → ¬ 𝜒 )
	mt3d.2	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
Assertion	mt3d	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		mt3d.1	⊢ ( 𝜑 → ¬ 𝜒 )
2		mt3d.2	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
3	2	con1d	⊢ ( 𝜑 → ( ¬ 𝜒 → 𝜓 ) )
4	1 3	mpd	⊢ ( 𝜑 → 𝜓 )