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Metamath Proof Explorer

Theorem ancrb

Description: Conjoin antecedent to right of consequent. (Contributed by NM, 25-Jul-1999) (Proof shortened by Wolf Lammen, 24-Mar-2013)

		Ref	Expression
	Assertion	ancrb	$⊢ (φ \to ψ) \leftrightarrow (φ \to (ψ \land φ))$

Step	Hyp	Ref	Expression
1		iba	$⊢ φ \to (ψ \leftrightarrow (ψ \land φ))$
2	1	pm5.74i	$⊢ (φ \to ψ) \leftrightarrow (φ \to (ψ \land φ))$