orimdi

Description: Disjunction distributes over implication. (Contributed by Wolf Lammen, 5-Jan-2013)

		Ref	Expression
	Assertion	orimdi	$⊢ (φ \lor (ψ \to χ)) \leftrightarrow ((φ \lor ψ) \to (φ \lor χ))$

Step	Hyp	Ref	Expression
1		imdi	$⊢ (\neg φ \to (ψ \to χ)) \leftrightarrow ((\neg φ \to ψ) \to (\neg φ \to χ))$
2		df-or	$⊢ (φ \lor (ψ \to χ)) \leftrightarrow (\neg φ \to (ψ \to χ))$
3		df-or	$⊢ (φ \lor ψ) \leftrightarrow (\neg φ \to ψ)$
4		df-or	$⊢ (φ \lor χ) \leftrightarrow (\neg φ \to χ)$
5	3 4	imbi12i	$⊢ ((φ \lor ψ) \to (φ \lor χ)) \leftrightarrow ((\neg φ \to ψ) \to (\neg φ \to χ))$
6	1 2 5	3bitr4i	$⊢ (φ \lor (ψ \to χ)) \leftrightarrow ((φ \lor ψ) \to (φ \lor χ))$

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