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Theorem ax5e 1711
Description: A rephrasing of ax-5 1709 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 ax-5 1709 . 2  |-  ( -. 
ph  ->  A. x  -.  ph )
2 eximal 1620 . 2  |-  ( ( E. x ph  ->  ph )  <->  ( -.  ph  ->  A. x  -.  ph ) )
31, 2mpbir 209 1  |-  ( E. x ph  ->  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1396   E.wex 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-5 1709
This theorem depends on definitions:  df-bi 185  df-ex 1618
This theorem is referenced by:  exlimiv  1727  exlimdv  1729  19.21v  1734  19.9v  1759  equid  1796  aev  1948  ac6s6f  30821  fnchoice  31644  bj-nfv  34628  bj-cbvexivw  34634  bj-snsetex  34922  bj-snglss  34929
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