Theorem bj-nnclavi 34421

Description: Inference associated with bj-nnclav 34420. Its associated inference is an instance of syl 17. Notice the non-intuitionistic proof from bj-peircei 34440 and bj-poni 34419. (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 34420	. 2 ⊢ (((𝜑 → 𝜓) → 𝜑) → ((𝜑 → 𝜓) → 𝜓))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → 𝜓) → 𝜓)

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by: (None)