Theorem bj-spst

Description: Closed form of sps . Once in main part, prove sps and spsd from it. (Contributed by BJ, 20-Oct-2019)

	Ref	Expression
Assertion	bj-spst	⊢ ( ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		sp	⊢ ( ∀ 𝑥 𝜑 → 𝜑 )
2	1	imim1i	⊢ ( ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 𝜑 → 𝜓 ) )