Theorem biantru

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 26-May-1993)

	Ref	Expression
Hypothesis	biantru.1	$$⊢\phi$$
Assertion	biantru	$$⊢\psi \leftrightarrow \left(\psi \wedge \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		biantru.1	$$⊢\phi$$
2		iba	$$⊢\phi \to \left(\psi \leftrightarrow \left(\psi \wedge \phi \right)\right)$$
3	1 2	ax-mp	$$⊢\psi \leftrightarrow \left(\psi \wedge \phi \right)$$