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	⊢ ( ( 𝜑 → 𝜓 ) → 𝜑 )
Assertion	bj-nnclavi	⊢ ( ( 𝜑 → 𝜓 ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bj-nnclavi.1	⊢ ( ( 𝜑 → 𝜓 ) → 𝜑 )
2		bj-nnclav	⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜑 ) → ( ( 𝜑 → 𝜓 ) → 𝜓 ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → 𝜓 ) → 𝜓 )