Theorem jad

Description: Deduction form of ja . (Contributed by Scott Fenton, 13-Dec-2010) (Proof shortened by Andrew Salmon, 17-Sep-2011)

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

Proof

Step	Hyp	Ref	Expression
1		jad.1	$$⊢\phi \to \left(\neg \psi \to \theta \right)$$
2		jad.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
3	1	com12	$$⊢\neg \psi \to \left(\phi \to \theta \right)$$
4	2	com12	$$⊢\chi \to \left(\phi \to \theta \right)$$
5	3 4	ja	$$⊢\left(\psi \to \chi \right)\to \left(\phi \to \theta \right)$$
6	5	com12	$$⊢\phi \to \left(\left(\psi \to \chi \right)\to \theta \right)$$