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Theorem bj-ceqsalg0 34854
Description: The FOL content of ceqsalg 3131. (Contributed by BJ, 12-Oct-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-ceqsalg0.1  |-  F/ x ps
bj-ceqsalg0.2  |-  ( ch 
->  ( ph  <->  ps )
)
Assertion
Ref Expression
bj-ceqsalg0  |-  ( E. x ch  ->  ( A. x ( ch  ->  ph )  <->  ps ) )

Proof of Theorem bj-ceqsalg0
StepHypRef Expression
1 bj-ceqsalg0.1 . 2  |-  F/ x ps
2 bj-ceqsalg0.2 . . 3  |-  ( ch 
->  ( ph  <->  ps )
)
32ax-gen 1623 . 2  |-  A. x
( ch  ->  ( ph 
<->  ps ) )
4 bj-ceqsalt0 34850 . 2  |-  ( ( F/ x ps  /\  A. x ( ch  ->  (
ph 
<->  ps ) )  /\  E. x ch )  -> 
( A. x ( ch  ->  ph )  <->  ps )
)
51, 3, 4mp3an12 1312 1  |-  ( E. x ch  ->  ( A. x ( ch  ->  ph )  <->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1396   E.wex 1617   F/wnf 1621
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-12 1859
This theorem depends on definitions:  df-bi 185  df-an 369  df-3an 973  df-ex 1618  df-nf 1622
This theorem is referenced by:  bj-ceqsalg  34855  bj-ceqsalgv  34857
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