Theorem jctild

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

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

Proof

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