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Theorem ax5e 1829
 Description: A rephrasing of ax-5 1827 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 1827 . 2 𝜑 → ∀𝑥 ¬ 𝜑)
2 eximal 1698 . 2 ((∃𝑥𝜑𝜑) ↔ (¬ 𝜑 → ∀𝑥 ¬ 𝜑))
31, 2mpbir 220 1 (∃𝑥𝜑𝜑)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1473  ∃wex 1695 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-5 1827 This theorem depends on definitions:  df-bi 196  df-ex 1696 This theorem is referenced by:  nfv  1830  exlimiv  1845  exlimdv  1848  19.21v  1855  19.9v  1883  aeveq  1969  aevOLD  2148  relopabi  5167  bj-ax5ea  31805  bj-cbvexivw  31847  bj-eqs  31850  bj-snsetex  32144  bj-snglss  32151  bj-toprntopon  32244  topdifinffinlem  32371  ac6s6f  33151  fnchoice  38211
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