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Theorem spsd 2185
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 2181 . 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 1535
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-12 2175
This theorem depends on definitions:  df-bi 207  df-ex 1777
This theorem is referenced by:  axc11v  2262  axc11rv  2263  equs5av  2275  equvel  2459  nfsb4t  2502  dfmoeu  2534  moexexlem  2624  2eu6  2655  zorn2lem4  10537  zorn2lem5  10538  axpowndlem3  10637  axacndlem5  10649  axc11n11r  36666  wl-equsal1i  37525  axc5c4c711  44397
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