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Theorem bnj1340 28856
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1340.1  |-  ( ps 
->  E. x th )
bnj1340.2  |-  ( ch  <->  ( ps  /\  th )
)
bnj1340.3  |-  ( ps 
->  A. x ps )
Assertion
Ref Expression
bnj1340  |-  ( ps 
->  E. x ch )

Proof of Theorem bnj1340
StepHypRef Expression
1 bnj1340.3 . . 3  |-  ( ps 
->  A. x ps )
2 bnj1340.1 . . 3  |-  ( ps 
->  E. x th )
31, 2bnj596 28775 . 2  |-  ( ps 
->  E. x ( ps 
/\  th ) )
4 bnj1340.2 . 2  |-  ( ch  <->  ( ps  /\  th )
)
53, 4bnj1198 28828 1  |-  ( ps 
->  E. x ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358   A.wal 1527   E.wex 1528
This theorem is referenced by:  bnj1450  29080
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
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