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Metamath Proof Explorer

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	$⊢ \neg φ \to χ$
	ja.2	$⊢ ψ \to χ$
Assertion	ja	$⊢ (φ \to ψ) \to χ$

Proof

Step	Hyp	Ref	Expression
1		ja.1	$⊢ \neg φ \to χ$
2		ja.2	$⊢ ψ \to χ$
3	2	imim2i	$⊢ (φ \to ψ) \to (φ \to χ)$
4	3 1	pm2.61d1	$⊢ (φ \to ψ) \to χ$