Theorem jca2r

Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 17-Oct-2010)

	Ref	Expression
Hypotheses	jca2r.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	jca2r.2	$$⊢\psi \to \theta$$
Assertion	jca2r	$$⊢\phi \to \left(\psi \to \left(\theta \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		jca2r.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		jca2r.2	$$⊢\psi \to \theta$$
3	2	a1i	$$⊢\phi \to \left(\psi \to \theta \right)$$
4	3 1	jcad	$$⊢\phi \to \left(\psi \to \left(\theta \wedge \chi \right)\right)$$