Theorem pm4.71i

Description: Inference converting an implication to a biconditional with conjunction. Inference from Theorem *4.71 of WhiteheadRussell p. 120. (Contributed by NM, 4-Jan-2004)

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

Proof

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