Theorem orcanai

Description: Change disjunction in consequent to conjunction in antecedent. (Contributed by NM, 8-Jun-1994)

	Ref	Expression
Hypothesis	orcanai.1	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ) )
Assertion	orcanai	⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		orcanai.1	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ) )
2	1	ord	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
3	2	imp	⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜒 )