Theorem bj-nnclavc

Description: Commuted form of bj-nnclav . Notice the non-intuitionistic proof from bj-peircei and imim1i . (Contributed by BJ, 30-Jul-2024) A proof which is shorter when compressed uses embantd . (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-nnclavc	⊢ ( ( 𝜑 → 𝜓 ) → ( ( ( 𝜑 → 𝜓 ) → 𝜑 ) → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		bj-nnclav	⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜑 ) → ( ( 𝜑 → 𝜓 ) → 𝜓 ) )
2	1	com12	⊢ ( ( 𝜑 → 𝜓 ) → ( ( ( 𝜑 → 𝜓 ) → 𝜑 ) → 𝜓 ) )