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Theorem 19.9v 2064
Description: Version of 19.9 2227 with a dv condition, requiring fewer axioms. Any formula can be existentially quantified using a variable which it does not contain. See also 19.3v 2065. (Contributed by NM, 28-May-1995.) Remove dependency on ax-7 2092. (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 1992 . 2 (∃𝑥𝜑𝜑)
2 19.8v 2063 . 2 (𝜑 → ∃𝑥𝜑)
31, 2impbii 199 1 (∃𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wex 1851
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056
This theorem depends on definitions:  df-bi 197  df-ex 1852
This theorem is referenced by:  19.3v  2065  19.23vOLD  2070  19.36v  2071  19.44v  2079  19.45v  2080  19.41vOLD  2081  zfcndpow  9639  volfiniune  30627  bnj937  31174  bnj594  31314  bnj907  31367  bnj1128  31390  bnj1145  31393  bj-sbfvv  33095  coss0  34564  prter2  34682  relopabVD  39653  rfcnnnub  39711
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