Theorem jao1i

Description: Add a disjunct in the antecedent of an implication. (Contributed by Rodolfo Medina, 24-Sep-2010)

	Ref	Expression
Hypothesis	jao1i.1	⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) )
Assertion	jao1i	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( 𝜒 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		jao1i.1	⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) )
2		ax-1	⊢ ( 𝜑 → ( 𝜒 → 𝜑 ) )
3	2 1	jaoi	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( 𝜒 → 𝜑 ) )