Theorem bj-nnclavci 37165

Description: Inference associated with bj-nnclavc 37164. Its associated inference is an instance of syl 18. Notice the non-intuitionistic proof from peirce 205 and syl 18. (Contributed by BJ, 30-Jul-2024.)

Hypothesis

Ref	Expression
bj-nnclavci.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
bj-nnclavci	⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜓)

Proof of Theorem bj-nnclavci

Step	Hyp	Ref	Expression
1		bj-nnclavci.1	. 2 ⊢ (𝜑 → 𝜓)
2		bj-nnclavc 37164	. 2 ⊢ ((𝜑 → 𝜓) → (((𝜑 → 𝜓) → 𝜑) → 𝜓))
3	1, 2	ax-mp 5	1 ⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜓)

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by: (None)