MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax5e Unicode version

Theorem ax5e 1706
Description: A rephrasing of ax-5 1704 using the existential quantifier. (Contributed by Wolf Lammen, 4-Dec-2017.)
Assertion
Ref Expression
ax5e
Distinct variable group:   ,

Proof of Theorem ax5e
StepHypRef Expression
1 ax-5 1704 . 2
2 eximal 1615 . 2
31, 2mpbir 209 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1393  E.wex 1612
This theorem is referenced by:  exlimiv  1722  exlimdv  1724  19.21v  1729  19.9v  1754  equid  1791  aev  1943  ac6s6f  30581  fnchoice  31404  bj-nfv  34227  bj-cbvexivw  34233  bj-snsetex  34521  bj-snglss  34528
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-5 1704
This theorem depends on definitions:  df-bi 185  df-ex 1613
  Copyright terms: Public domain W3C validator