Theorem jca32

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

	Ref	Expression
Hypotheses	jca31.1	$$⊢\phi \to \psi$$
	jca31.2	$$⊢\phi \to \chi$$
	jca31.3	$$⊢\phi \to \theta$$
Assertion	jca32	$$⊢\phi \to \left(\psi \wedge \left(\chi \wedge \theta \right)\right)$$

Proof

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