Theorem jca31

Description: Join three consequents. (Contributed by Jeff Hankins, 1-Aug-2009)

	Ref	Expression
Hypotheses	jca31.1	$$⊢\phi \to \psi$$
	jca31.2	$$⊢\phi \to \chi$$
	jca31.3	$$⊢\phi \to \theta$$
Assertion	jca31	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\wedge \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		jca31.1	$$⊢\phi \to \psi$$
2		jca31.2	$$⊢\phi \to \chi$$
3		jca31.3	$$⊢\phi \to \theta$$
4	1 2	jca	$$⊢\phi \to \left(\psi \wedge \chi \right)$$
5	4 3	jca	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\wedge \theta \right)$$