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Theorem 19.9v 1953
 Description: Version of 19.9 2110 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 1954. (Contributed by NM, 28-May-1995.) Remove dependency on ax-7 1981. (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 1881 . 2 (∃𝑥𝜑𝜑)
2 19.8v 1952 . 2 (𝜑 → ∃𝑥𝜑)
31, 2impbii 199 1 (∃𝑥𝜑𝜑)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196  ∃wex 1744 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945 This theorem depends on definitions:  df-bi 197  df-ex 1745 This theorem is referenced by:  19.3v  1954  19.23vOLD  1959  19.36v  1960  19.44v  1968  19.45v  1969  19.41vOLD  1970  elsnxpOLD  5716  zfcndpow  9476  volfiniune  30421  bnj937  30968  bnj594  31108  bnj907  31161  bnj1128  31184  bnj1145  31187  bj-sbfvv  32890  coss0  34369  prter2  34485  relopabVD  39451  rfcnnnub  39509
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