Theorem biantrur

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 3-Aug-1994)

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

Proof

Step	Hyp	Ref	Expression
1		biantrur.1	$$⊢\phi$$
2	1	biantru	$$⊢\psi \leftrightarrow \left(\psi \wedge \phi \right)$$
3	2	biancomi	$$⊢\psi \leftrightarrow \left(\phi \wedge \psi \right)$$