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Theorem 19.3v 1991
Description: Version of 19.3 2204 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 1993. (Contributed by Anthony Hart, 13-Sep-2011.) Remove dependency on ax-7 2020. (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 1990 . 2 (∀𝑥𝜑𝜑)
2 ax-5 1917 . 2 (𝜑 → ∀𝑥𝜑)
31, 2impbii 212 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975
This theorem depends on definitions:  df-bi 210  df-ex 1787
This theorem is referenced by:  spvwOLD  1995  19.27v  2001  19.28v  2002  19.37v  2003  axrep1  5165  axrep6  5171  kmlem14  9675  zfcndrep  10126  zfcndpow  10128  zfcndac  10131  lfuhgr3  32664  bj-snsetex  34808  iooelexlt  35188  dford4  40463  relexp0eq  40895
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