Theorem pm4.71ri

Description: Inference converting an implication to a biconditional with conjunction. Inference from Theorem *4.71 of WhiteheadRussell p. 120 (with conjunct reversed). (Contributed by NM, 1-Dec-2003)

	Ref	Expression
Hypothesis	pm4.71ri.1	$$⊢\phi \to \psi$$
Assertion	pm4.71ri	$$⊢\phi \leftrightarrow \left(\psi \wedge \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm4.71ri.1	$$⊢\phi \to \psi$$
2	1	pm4.71i	$$⊢\phi \leftrightarrow \left(\phi \wedge \psi \right)$$
3	2	biancomi	$$⊢\phi \leftrightarrow \left(\psi \wedge \phi \right)$$