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

Metamath Proof Explorer

Theorem 3expa

Description: Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995) (Revised to shorten 3exp and pm3.2an3 by Wolf Lammen, 22-Jun-2022.)

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

Proof

Step	Hyp	Ref	Expression
1		3exp.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	sylbir	$⊢ ((φ \land ψ) \land χ) \to θ$