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Theorem 19.9v 1988
Description: Version of 19.9 2199 with a disjoint variable condition, requiring fewer axioms. Any formula can be existentially quantified using a variable which it does not contain. See also 19.3v 1986. (Contributed by NM, 28-May-1995.) Remove dependency on ax-7 2012. (Revised by Wolf Lammen, 4-Dec-2017.)
Assertion
Ref Expression
19.9v (∃𝑥𝜑𝜑)
Distinct variable group:   𝜑,𝑥

Proof of Theorem 19.9v
StepHypRef Expression
1 ax5e 1916 . 2 (∃𝑥𝜑𝜑)
2 19.8v 1987 . 2 (𝜑 → ∃𝑥𝜑)
31, 2impbii 208 1 (∃𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wex 1782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972
This theorem depends on definitions:  df-bi 206  df-ex 1783
This theorem is referenced by:  19.36v  1992  19.44v  1997  19.45v  1998  zfcndpow  10611  volfiniune  33228  bnj937  33782  bnj594  33923  bnj907  33978  bnj1128  34001  bnj1145  34004  coss0  37349  prter2  37751  relopabVD  43662  rfcnnnub  43720
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