This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ φ \to ψ$
	Assertion	biantrud	$⊢ φ \to (χ \leftrightarrow (χ \land ψ))$

Step	Hyp	Ref	Expression
1		biantrud.1	$⊢ φ \to ψ$
2		iba	$⊢ ψ \to (χ \leftrightarrow (χ \land ψ))$
3	1 2	syl	$⊢ φ \to (χ \leftrightarrow (χ \land ψ))$