Theorem jcad

Description: Deduction conjoining the consequents of two implications. Deduction form of jca and double deduction form of pm3.2 and pm3.2i . (Contributed by NM, 15-Jul-1993) (Proof shortened by Wolf Lammen, 23-Jul-2013)

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

Proof

Step	Hyp	Ref	Expression
1		jcad.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		jcad.2	$$⊢\phi \to \left(\psi \to \theta \right)$$
3		pm3.2	$$⊢\chi \to \left(\theta \to \left(\chi \wedge \theta \right)\right)$$
4	1 2 3	syl6c	$$⊢\phi \to \left(\psi \to \left(\chi \wedge \theta \right)\right)$$