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	⊢ ( ¬ 𝜑 → 𝜒 )
	ja.2	⊢ ( 𝜓 → 𝜒 )
Assertion	ja	⊢ ( ( 𝜑 → 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		ja.1	⊢ ( ¬ 𝜑 → 𝜒 )
2		ja.2	⊢ ( 𝜓 → 𝜒 )
3	2	imim2i	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) )
4	3 1	pm2.61d1	⊢ ( ( 𝜑 → 𝜓 ) → 𝜒 )