Theorem mt2d

Description: Modus tollens deduction. (Contributed by NM, 4-Jul-1994)

	Ref	Expression
Hypotheses	mt2d.1	⊢ ( 𝜑 → 𝜒 )
	mt2d.2	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) )
Assertion	mt2d	⊢ ( 𝜑 → ¬ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		mt2d.1	⊢ ( 𝜑 → 𝜒 )
2		mt2d.2	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) )
3	2	con2d	⊢ ( 𝜑 → ( 𝜒 → ¬ 𝜓 ) )
4	1 3	mpd	⊢ ( 𝜑 → ¬ 𝜓 )