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Metamath Proof Explorer

Theorem pm5.74da

Description: Distribution of implication over biconditional (deduction form). Variant of pm5.74d . (Contributed by NM, 4-May-2007)

		Ref	Expression
	Hypothesis	pm5.74da.1	$⊢ (φ \land ψ) \to (χ \leftrightarrow θ)$
	Assertion	pm5.74da	$⊢ φ \to ((ψ \to χ) \leftrightarrow (ψ \to θ))$

Step	Hyp	Ref	Expression
1		pm5.74da.1	$⊢ (φ \land ψ) \to (χ \leftrightarrow θ)$
2	1	ex	$⊢ φ \to (ψ \to (χ \leftrightarrow θ))$
3	2	pm5.74d	$⊢ φ \to ((ψ \to χ) \leftrightarrow (ψ \to θ))$