Theorem jctir

Description: Inference conjoining a theorem to right of consequent in an implication. (Contributed by NM, 31-Dec-1993)

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

Proof

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