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Theorem bj-spst 32654
Description: Closed form of sps 2053. Once in main part, prove sps 2053 and spsd 2055 from it. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-spst ((𝜑𝜓) → (∀𝑥𝜑𝜓))

Proof of Theorem bj-spst
StepHypRef Expression
1 sp 2051 . 2 (∀𝑥𝜑𝜑)
21imim1i 63 1 ((𝜑𝜓) → (∀𝑥𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1479
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-12 2045
This theorem depends on definitions:  df-bi 197  df-ex 1703
This theorem is referenced by: (None)
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