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Metamath Proof Explorer

Theorem biantrur

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

		Ref	Expression
	Hypothesis	biantrur.1	$⊢ φ$
	Assertion	biantrur	$⊢ ψ \leftrightarrow (φ \land ψ)$

Step	Hyp	Ref	Expression
1		biantrur.1	$⊢ φ$
2	1	biantru	$⊢ ψ \leftrightarrow (ψ \land φ)$
3	2	biancomi	$⊢ ψ \leftrightarrow (φ \land ψ)$