Theorem bj-nnclavci

Description: Inference associated with bj-nnclavc . Its associated inference is an instance of syl . Notice the non-intuitionistic proof from peirce and syl . (Contributed by BJ, 30-Jul-2024)

	Ref	Expression
Hypothesis	bj-nnclavci.1	$$⊢\phi \to \psi$$
Assertion	bj-nnclavci	$$⊢\left(\left(\phi \to \psi \right)\to \phi \right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		bj-nnclavci.1	$$⊢\phi \to \psi$$
2		bj-nnclavc	$$⊢\left(\phi \to \psi \right)\to \left(\left(\left(\phi \to \psi \right)\to \phi \right)\to \psi \right)$$
3	1 2	ax-mp	$$⊢\left(\left(\phi \to \psi \right)\to \phi \right)\to \psi$$