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

Proof

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