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Theorem 19.3v 1987
 Description: Version of 19.3 2203 with a disjoint variable condition, requiring fewer axioms. Any formula can be universally quantified using a variable which it does not contain. See also 19.9v 1989. (Contributed by Anthony Hart, 13-Sep-2011.) Remove dependency on ax-7 2016. (Revised by Wolf Lammen, 4-Dec-2017.) (Proof shortened by Wolf Lammen, 20-Oct-2023.)
Assertion
Ref Expression
19.3v (∀𝑥𝜑𝜑)
Distinct variable group:   𝜑,𝑥

Proof of Theorem 19.3v
StepHypRef Expression
1 spvw 1986 . 2 (∀𝑥𝜑𝜑)
2 ax-5 1912 . 2 (𝜑 → ∀𝑥𝜑)
31, 2impbii 212 1 (∀𝑥𝜑𝜑)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209  ∀wal 1536 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971 This theorem depends on definitions:  df-bi 210  df-ex 1782 This theorem is referenced by:  spvwOLD  1991  19.27v  1997  19.28v  1998  19.37v  1999  axrep1  5164  axrep6  5170  kmlem14  9566  zfcndrep  10013  zfcndpow  10015  zfcndac  10018  lfuhgr3  32374  bj-snsetex  34293  iooelexlt  34663  dford4  39777  relexp0eq  40209
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