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Metamath Proof Explorer

Theorem jao1i

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

		Ref	Expression
	Hypothesis	jao1i.1	$⊢ ψ \to (χ \to φ)$
	Assertion	jao1i	$⊢ (φ \lor ψ) \to (χ \to φ)$

Step	Hyp	Ref	Expression
1		jao1i.1	$⊢ ψ \to (χ \to φ)$
2		ax-1	$⊢ φ \to (χ \to φ)$
3	2 1	jaoi	$⊢ (φ \lor ψ) \to (χ \to φ)$