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Theorem exbi 1643
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 bi1 186 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
21aleximi 1632 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ph  ->  E. x ps )
)
3 bi2 198 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
43aleximi 1632 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ps 
->  E. x ph )
)
52, 4impbid 191 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 1377   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by:  exbii  1644  exbidh  1653  exintrbi  1677  19.19  1906  2exbi  30863  rexbidar  30933  onfrALTlem5VD  32765  onfrALTlem1VD  32770  csbxpgVD  32774  csbrngVD  32776  csbunigVD  32778  e2ebindVD  32792  e2ebindALT  32809  bnj956  32914  bj-2exbi  33293  bj-3exbi  33294  bj-nfbi  33305
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