Theorem orrd

Description: Deduce disjunction from implication. (Contributed by NM, 27-Nov-1995)

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

Proof

Step	Hyp	Ref	Expression
1		orrd.1	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
2		pm2.54	⊢ ( ( ¬ 𝜓 → 𝜒 ) → ( 𝜓 ∨ 𝜒 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ) )