Theorem biantrurd

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 1-May-1995) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Hypothesis	biantrud.1	$$⊢\phi \to \psi$$
Assertion	biantrurd	$$⊢\phi \to \left(\chi \leftrightarrow \left(\psi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		biantrud.1	$$⊢\phi \to \psi$$
2		ibar	$$⊢\psi \to \left(\chi \leftrightarrow \left(\psi \wedge \chi \right)\right)$$
3	1 2	syl	$$⊢\phi \to \left(\chi \leftrightarrow \left(\psi \wedge \chi \right)\right)$$