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Theorem bj-biexal2 31261
Description: A general FOL biconditional. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-biexal2  |-  ( A. x ( E. x ph  ->  ps )  <->  ( E. x ph  ->  A. x ps ) )

Proof of Theorem bj-biexal2
StepHypRef Expression
1 nfe1 1894 . 2  |-  F/ x E. x ph
2119.21 1964 1  |-  ( A. x ( E. x ph  ->  ps )  <->  ( E. x ph  ->  A. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   A.wal 1435   E.wex 1657
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-ex 1658  df-nf 1662
This theorem is referenced by:  bj-biexal3  31262
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