Theorem jccir

Description: Inference conjoining a consequent of a consequent to the right of the consequent in an implication. See also ex-natded5.3i . (Contributed by Mario Carneiro, 9-Feb-2017) (Revised by AV, 20-Aug-2019)

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

Proof

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