Theorem pm2.18da

Description: Deduction based on reductio ad absurdum. See pm2.18 . (Contributed by Mario Carneiro, 9-Feb-2017)

	Ref	Expression
Hypothesis	pm2.18da.1	⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜓 )
Assertion	pm2.18da	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		pm2.18da.1	⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜓 )
2	1	ex	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜓 ) )
3	2	pm2.18d	⊢ ( 𝜑 → 𝜓 )