Theorem iba

Description: Introduction of antecedent as conjunct. Theorem *4.73 of WhiteheadRussell p. 121. (Contributed by NM, 30-Mar-1994)

	Ref	Expression
Assertion	iba	$$⊢\phi \to \left(\psi \leftrightarrow \left(\psi \wedge \phi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm3.21	$$⊢\phi \to \left(\psi \to \left(\psi \wedge \phi \right)\right)$$
2		simpl	$$⊢\left(\psi \wedge \phi \right)\to \psi$$
3	1 2	impbid1	$$⊢\phi \to \left(\psi \leftrightarrow \left(\psi \wedge \phi \right)\right)$$