Theorem orri

Description: Infer disjunction from implication. (Contributed by NM, 11-Jun-1994)

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

Proof

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