Theorem bj-nnclavi 37163

Description: Inference associated with bj-nnclav 37162. Its associated inference is an instance of syl 18. Notice the non-intuitionistic proof from bj-peircei 37185 and bj-poni 37161. (Contributed by BJ, 30-Jul-2024.)

Hypothesis

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

Assertion

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

Proof of Theorem bj-nnclavi

Step	Hyp	Ref	Expression
1		bj-nnclavi.1	. 2 ⊢ ((𝜑 → 𝜓) → 𝜑)
2		bj-nnclav 37162	. 2 ⊢ (((𝜑 → 𝜓) → 𝜑) → ((𝜑 → 𝜓) → 𝜓))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → 𝜓) → 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)