Metamath Proof Explorer


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 ( ( 𝜑𝜓 ) → ( ∀ 𝑥 𝜑𝜓 ) )

Proof

Step Hyp Ref Expression
1 sp ( ∀ 𝑥 𝜑𝜑 )
2 1 imim1i ( ( 𝜑𝜓 ) → ( ∀ 𝑥 𝜑𝜓 ) )