Theorem pm3.2an3

Description: Version of pm3.2 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011) (Proof shortened by Kyle Wyonch, 24-Apr-2021) (Proof shortened by Wolf Lammen, 21-Jun-2022)

	Ref	Expression
Assertion	pm3.2an3	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\phi \wedge \psi \wedge \chi \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\phi \wedge \psi \wedge \chi \right)$$
2	1	3exp	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\phi \wedge \psi \wedge \chi \right)\right)\right)$$