Metamath Proof Explorer

Theorem 3impa

Description: Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995) (Revised to shorten 3imp by Wolf Lammen, 20-Jun-2022.)

		Ref	Expression
	Hypothesis	3impa.1	$⊢ ((φ \land ψ) \land χ) \to θ$
	Assertion	3impa	$⊢ (φ \land ψ \land χ) \to θ$

Proof

Step	Hyp	Ref	Expression
1		3impa.1	$⊢ ((φ \land ψ) \land χ) \to θ$
2		df-3an	$⊢ (φ \land ψ \land χ) \leftrightarrow ((φ \land ψ) \land χ)$
3	2 1	sylbi	$⊢ (φ \land ψ \land χ) \to θ$