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Theorem bnj1275 29259
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1275.1  |-  ( ph  ->  E. x ( ps 
/\  ch ) )
bnj1275.2  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
bnj1275  |-  ( ph  ->  E. x ( ph  /\ 
ps  /\  ch )
)

Proof of Theorem bnj1275
StepHypRef Expression
1 bnj1275.2 . . 3  |-  ( ph  ->  A. x ph )
2 bnj1275.1 . . 3  |-  ( ph  ->  E. x ( ps 
/\  ch ) )
31, 2bnj596 29188 . 2  |-  ( ph  ->  E. x ( ph  /\  ( ps  /\  ch ) ) )
4 3anass 941 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ( ps  /\  ch ) ) )
53, 4bnj1198 29241 1  |-  ( ph  ->  E. x ( ph  /\ 
ps  /\  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    /\ w3a 937   A.wal 1550   E.wex 1551
This theorem is referenced by:  bnj1345  29270  bnj1279  29461
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-ex 1552  df-nf 1555
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