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Theorem spsd 2178
 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 2174 . 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 1528 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-12 2169 This theorem depends on definitions:  df-bi 208  df-ex 1774 This theorem is referenced by:  axc11v  2258  axc11rv  2259  equs5av  2273  equvel  2476  nfsb4t  2537  nfsb4tALT  2602  dfmoeu  2616  moexexlem  2710  2eu6  2743  zorn2lem4  9910  zorn2lem5  9911  axpowndlem3  10010  axacndlem5  10022  axc11n11r  33901  wl-equsal1i  34651  axc5c4c711  40598
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