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Theorem ax5e 1682
Description: A rephrasing of ax-5 1680 using the existential quantifier. (Contributed by Wolf Lammen, 4-Dec-2017.)
Assertion
Ref Expression
ax5e  |-  ( E. x ph  ->  ph )
Distinct variable group:    ph, x

Proof of Theorem ax5e
StepHypRef Expression
1 df-ex 1597 . 2  |-  ( E. x ph  <->  -.  A. x  -.  ph )
2 ax-5 1680 . . 3  |-  ( -. 
ph  ->  A. x  -.  ph )
32con1i 129 . 2  |-  ( -. 
A. x  -.  ph  ->  ph )
41, 3sylbi 195 1  |-  ( E. x ph  ->  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1377   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-5 1680
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by:  exlimiv  1698  exlimdv  1700  19.9v  1728  equid  1740  aev  1890  19.21v  1930  ac6s6f  30213  fnchoice  31010  bj-nfv  33327  bj-snsetex  33620  bj-snglss  33627
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