Theorem jarr

Description: Elimination of a nested antecedent. Sometimes called "Syll-Simp" since it is a syllogism applied to ax-1 ("Simplification"). (Contributed by Wolf Lammen, 9-May-2013)

	Ref	Expression
Assertion	jarr	$$⊢\left(\left(\phi \to \psi \right)\to \chi \right)\to \left(\psi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-1	$$⊢\psi \to \left(\phi \to \psi \right)$$
2	1	imim1i	$$⊢\left(\left(\phi \to \psi \right)\to \chi \right)\to \left(\psi \to \chi \right)$$