Theorem pm2.65d

Description: Deduction for proof by contradiction. (Contributed by NM, 26-Jun-1994) (Proof shortened by Wolf Lammen, 26-May-2013)

	Ref	Expression
Hypotheses	pm2.65d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	pm2.65d.2	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) )
Assertion	pm2.65d	⊢ ( 𝜑 → ¬ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		pm2.65d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		pm2.65d.2	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) )
3	2 1	nsyld	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜓 ) )
4	3	pm2.01d	⊢ ( 𝜑 → ¬ 𝜓 )