Theorem pm2.65da

Description: Deduction for proof by contradiction. (Contributed by NM, 12-Jun-2014)

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

Proof

Step	Hyp	Ref	Expression
1		pm2.65da.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2		pm2.65da.2	⊢ ( ( 𝜑 ∧ 𝜓 ) → ¬ 𝜒 )
3	1	ex	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	2	ex	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) )
5	3 4	pm2.65d	⊢ ( 𝜑 → ¬ 𝜓 )