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Theorem spsd 2095
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 2091 . 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 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-ex 1745
This theorem is referenced by:  axc11v  2176  axc11rv  2177  axc11rvOLD  2178  equvel  2375  nfsb4t  2417  mo2v  2505  moexex  2570  2eu6  2587  zorn2lem4  9359  zorn2lem5  9360  axpowndlem3  9459  axacndlem5  9471  axc11n11r  32798  wl-equsal1i  33459  axc5c4c711  38919
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