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Metamath Proof Explorer

Theorem pm4.71rd

Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of WhiteheadRussell p. 120. (Contributed by NM, 10-Feb-2005)

		Ref	Expression
	Hypothesis	pm4.71rd.1	$⊢ φ \to (ψ \to χ)$
	Assertion	pm4.71rd	$⊢ φ \to (ψ \leftrightarrow (χ \land ψ))$

Proof

Step	Hyp	Ref	Expression
1		pm4.71rd.1	$⊢ φ \to (ψ \to χ)$
2	1	pm4.71d	$⊢ φ \to (ψ \leftrightarrow (ψ \land χ))$
3	2	biancomd	$⊢ φ \to (ψ \leftrightarrow (χ \land ψ))$