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Theorem spsd 2219
Description: Deduction generalizing antecedent. (Contributed by NM, 17-Aug-1994.)
Hypothesis
Ref Expression
spsd.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
spsd (𝜑 → (∀𝑥𝜓𝜒))

Proof of Theorem spsd
StepHypRef Expression
1 sp 2215 . 2 (∀𝑥𝜓𝜓)
2 spsd.1 . 2 (𝜑 → (𝜓𝜒))
31, 2syl5 34 1 (𝜑 → (∀𝑥𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1650
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2069  ax-7 2105  ax-12 2211
This theorem depends on definitions:  df-bi 198  df-ex 1875
This theorem is referenced by:  axc11v  2313  axc11rv  2314  equvel  2434  nfsb4t  2477  dfmo  2598  moexex  2662  2eu6  2679  zorn2lem4  9573  zorn2lem5  9574  axpowndlem3  9673  axacndlem5  9685  axc11n11r  33040  wl-equsal1i  33686  axc5c4c711  39207
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