Theorem bj-spst 34871

Description: Closed form of sps 2178. Once in main part, prove sps 2178 and spsd 2180 from it. (Contributed by BJ, 20-Oct-2019.)

Assertion

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

Proof of Theorem bj-spst

Step	Hyp	Ref	Expression
1		sp 2176	. 2 ⊢ (∀𝑥𝜑 → 𝜑)
2	1	imim1i 63	1 ⊢ ((𝜑 → 𝜓) → (∀𝑥𝜑 → 𝜓))

Syntax hints:   → wi 4  ∀wal 1537

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171

This theorem depends on definitions:  df-bi 206  df-ex 1783

This theorem is referenced by: (None)