Theorem mtod

Description: Modus tollens deduction. (Contributed by NM, 3-Apr-1994) (Proof shortened by Wolf Lammen, 11-Sep-2013)

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

Proof

Step	Hyp	Ref	Expression
1		mtod.1	⊢ ( 𝜑 → ¬ 𝜒 )
2		mtod.2	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3	1	a1d	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) )
4	2 3	pm2.65d	⊢ ( 𝜑 → ¬ 𝜓 )