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Theorem bj-exnalimn 32467
Description: A transformation of quantifiers and logical connectives. The general statement that equs3 1697 proves. (Contributed by BJ, 29-Sep-2019.)
Assertion
Ref Expression
bj-exnalimn  |-  ( E. x ( ph  /\  ps )  <->  -.  A. x
( ph  ->  -.  ps ) )

Proof of Theorem bj-exnalimn
StepHypRef Expression
1 alinexa 1631 . 2  |-  ( A. x ( ph  ->  -. 
ps )  <->  -.  E. x
( ph  /\  ps )
)
21con2bii 332 1  |-  ( E. x ( ph  /\  ps )  <->  -.  A. x
( ph  ->  -.  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    /\ wa 369   A.wal 1368   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588
This theorem is referenced by: (None)
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