Theorem bj-nnclavi

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

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

Proof

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