Theorem ja

Description: Inference joining the antecedents of two premises. For partial converses, see jarri and jarli . (Contributed by NM, 24-Jan-1993) (Proof shortened by Mel L. O'Cat, 19-Feb-2008)

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

Proof

Step	Hyp	Ref	Expression
1		ja.1	$$⊢\neg \phi \to \chi$$
2		ja.2	$$⊢\psi \to \chi$$
3	2	imim2i	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)$$
4	3 1	pm2.61d1	$$⊢\left(\phi \to \psi \right)\to \chi$$