Theorem jca2

Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 12-Oct-2010)

	Ref	Expression
Hypotheses	jca2.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	jca2.2	$$⊢\psi \to \theta$$
Assertion	jca2	$$⊢\phi \to \left(\psi \to \left(\chi \wedge \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		jca2.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		jca2.2	$$⊢\psi \to \theta$$
3	2	a1i	$$⊢\phi \to \left(\psi \to \theta \right)$$
4	1 3	jcad	$$⊢\phi \to \left(\psi \to \left(\chi \wedge \theta \right)\right)$$