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Theorem bj-eeanvw 31373
Description: Version of eeanv 2093 with a DV condition on  x ,  y not requiring ax-11 1937. (The same can be done with eeeanv 2094 and ee4anv 2095.) (Contributed by BJ, 29-Sep-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-eeanvw  |-  ( E. x E. y (
ph  /\  ps )  <->  ( E. x ph  /\  E. y ps ) )
Distinct variable groups:    ph, y    ps, x    x, y
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem bj-eeanvw
StepHypRef Expression
1 19.42v 1842 . . 3  |-  ( E. y ( ph  /\  ps )  <->  ( ph  /\  E. y ps ) )
21exbii 1726 . 2  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( ph  /\  E. y ps ) )
3 19.41v 1838 . 2  |-  ( E. x ( ph  /\  E. y ps )  <->  ( E. x ph  /\  E. y ps ) )
42, 3bitri 257 1  |-  ( E. x E. y (
ph  /\  ps )  <->  ( E. x ph  /\  E. y ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 189    /\ wa 376   E.wex 1671
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672
This theorem is referenced by: (None)
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