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Theorem exbi 1687
Description: Theorem 19.18 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
exbi  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ph  <->  E. x ps ) )

Proof of Theorem exbi
StepHypRef Expression
1 biimp 193 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
21aleximi 1674 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ph  ->  E. x ps )
)
3 biimpr 198 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
43aleximi 1674 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ps 
->  E. x ph )
)
52, 4impbid 190 1  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ph  <->  E. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1403   E.wex 1633
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652
This theorem depends on definitions:  df-bi 185  df-ex 1634
This theorem is referenced by:  exbii  1688  exbidh  1697  exintrbi  1722  19.19  1987  bnj956  29162  bj-2exbi  30770  bj-3exbi  30771  bj-nfbi  30781  2exbi  36133  rexbidar  36203  onfrALTlem5VD  36716  onfrALTlem1VD  36721  csbxpgVD  36725  csbrngVD  36727  csbunigVD  36729  e2ebindVD  36743  e2ebindALT  36760
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