Theorem pm4.45im

Description: Conjunction with implication. Compare Theorem *4.45 of WhiteheadRussell p. 119. (Contributed by NM, 17-May-1998)

	Ref	Expression
Assertion	pm4.45im	$$⊢\phi \leftrightarrow \left(\phi \wedge \left(\psi \to \phi \right)\right)$$

Proof

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