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	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
Assertion	3impa	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		3impa.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
2		df-3an	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\wedge \chi \right)$$
3	2 1	sylbi	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$