Theorem bj-poni 37190

Description: Inference associated with "pon", pm2.27 43. Its associated inference is ax-mp 5. (Contributed by BJ, 30-Jul-2024.)

Hypothesis

Ref	Expression
bj-poni.1	⊢ 𝜑

Assertion

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

Proof of Theorem bj-poni

Step	Hyp	Ref	Expression
1		bj-poni.1	. 2 ⊢ 𝜑
2		pm2.27 43	. 2 ⊢ (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)