Theorem mt2

Description: A rule similar to modus tollens. Inference associated with con2i . (Contributed by NM, 19-Aug-1993) (Proof shortened by Wolf Lammen, 10-Sep-2013)

	Ref	Expression
Hypotheses	mt2.1	⊢ 𝜓
	mt2.2	⊢ ( 𝜑 → ¬ 𝜓 )
Assertion	mt2	⊢ ¬ 𝜑

Proof

Step	Hyp	Ref	Expression
1		mt2.1	⊢ 𝜓
2		mt2.2	⊢ ( 𝜑 → ¬ 𝜓 )
3	1	a1i	⊢ ( 𝜑 → 𝜓 )
4	3 2	pm2.65i	⊢ ¬ 𝜑