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	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	pm4.71rd	$$⊢\phi \to \left(\psi \leftrightarrow \left(\chi \wedge \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm4.71rd.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	pm4.71d	$$⊢\phi \to \left(\psi \leftrightarrow \left(\psi \wedge \chi \right)\right)$$
3	2	biancomd	$$⊢\phi \to \left(\psi \leftrightarrow \left(\chi \wedge \psi \right)\right)$$