Metamath Proof Explorer

Theorem dedlem0a

Description: Lemma for an alternate version of weak deduction theorem. (Contributed by NM, 2-Apr-1994) (Proof shortened by Andrew Salmon, 7-May-2011) (Proof shortened by Wolf Lammen, 4-Dec-2012)

		Ref	Expression
	Assertion	dedlem0a	$⊢ φ \to (ψ \leftrightarrow ((χ \to φ) \to (ψ \land φ)))$

Proof

Step	Hyp	Ref	Expression
1		iba	$⊢ φ \to (ψ \leftrightarrow (ψ \land φ))$
2		biimt	$⊢ (χ \to φ) \to ((ψ \land φ) \leftrightarrow ((χ \to φ) \to (ψ \land φ)))$
3	2	jarri	$⊢ φ \to ((ψ \land φ) \leftrightarrow ((χ \to φ) \to (ψ \land φ)))$
4	1 3	bitrd	$⊢ φ \to (ψ \leftrightarrow ((χ \to φ) \to (ψ \land φ)))$