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Theorem spsd 2210
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 2206 . 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 1628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-12 2202
This theorem depends on definitions:  df-bi 197  df-ex 1852
This theorem is referenced by:  axc11v  2302  axc11rv  2303  axc11rvOLD  2304  equvel  2492  nfsb4t  2535  mo2v  2624  moexex  2689  2eu6  2706  zorn2lem4  9522  zorn2lem5  9523  axpowndlem3  9622  axacndlem5  9634  axc11n11r  33004  wl-equsal1i  33657  axc5c4c711  39121
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