Theorem mtand

Description: A modus tollens deduction. (Contributed by Jeff Hankins, 19-Aug-2009)

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

Proof

Step	Hyp	Ref	Expression
1		mtand.1	⊢ ( 𝜑 → ¬ 𝜒 )
2		mtand.2	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
3	2	ex	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	1 3	mtod	⊢ ( 𝜑 → ¬ 𝜓 )