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Theorem ax5e 1839
Description: A rephrasing of ax-5 1837 using the existential quantifier. (Contributed by Wolf Lammen, 4-Dec-2017.)
Assertion
Ref Expression
ax5e (∃𝑥𝜑𝜑)
Distinct variable group:   𝜑,𝑥

Proof of Theorem ax5e
StepHypRef Expression
1 ax-5 1837 . 2 𝜑 → ∀𝑥 ¬ 𝜑)
2 eximal 1705 . 2 ((∃𝑥𝜑𝜑) ↔ (¬ 𝜑 → ∀𝑥 ¬ 𝜑))
31, 2mpbir 221 1 (∃𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1479  wex 1702
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-5 1837
This theorem depends on definitions:  df-bi 197  df-ex 1703
This theorem is referenced by:  ax5ea  1840  exlimiv  1856  exlimdv  1859  19.21v  1866  19.9v  1894  aeveq  1980  aevOLD  2160  relopabi  5234  toprntopon  20710  bj-cbvexivw  32635  bj-eqs  32638  bj-snsetex  32926  bj-snglss  32933  topdifinffinlem  33166  ac6s6f  33952  fnchoice  39008
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