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Theorem bj-spst 33016
Description: Closed form of sps 2209. Once in main part, prove sps 2209 and spsd 2211 from it. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-spst ((𝜑𝜓) → (∀𝑥𝜑𝜓))

Proof of Theorem bj-spst
StepHypRef Expression
1 sp 2207 . 2 (∀𝑥𝜑𝜑)
21imim1i 63 1 ((𝜑𝜓) → (∀𝑥𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1629
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-ex 1853
This theorem is referenced by: (None)
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