Theorem biantrud

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 2-Aug-1994) (Proof shortened by Wolf Lammen, 23-Oct-2013)

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

Proof

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