Theorem jctird

Description: Deduction conjoining a theorem to right of consequent in an implication. (Contributed by NM, 21-Apr-2005)

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

Proof

Step	Hyp	Ref	Expression
1		jctird.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		jctird.2	$$⊢\phi \to \theta$$
3	2	a1d	$$⊢\phi \to \left(\psi \to \theta \right)$$
4	1 3	jcad	$$⊢\phi \to \left(\psi \to \left(\chi \wedge \theta \right)\right)$$