Theorem ord

Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994)

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

Proof

Step	Hyp	Ref	Expression
1		ord.1	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ) )
2		df-or	⊢ ( ( 𝜓 ∨ 𝜒 ) ↔ ( ¬ 𝜓 → 𝜒 ) )
3	1 2	sylib	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )