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Theorem bnj596 29176
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj596.1  |-  ( ph  ->  A. x ph )
bnj596.2  |-  ( ph  ->  E. x ps )
Assertion
Ref Expression
bnj596  |-  ( ph  ->  E. x ( ph  /\ 
ps ) )

Proof of Theorem bnj596
StepHypRef Expression
1 bnj596.2 . . 3  |-  ( ph  ->  E. x ps )
21ancli 536 . 2  |-  ( ph  ->  ( ph  /\  E. x ps ) )
3 bnj596.1 . . . 4  |-  ( ph  ->  A. x ph )
43nfi 1561 . . 3  |-  F/ x ph
5419.42 1903 . 2  |-  ( E. x ( ph  /\  ps )  <->  ( ph  /\  E. x ps ) )
62, 5sylibr 205 1  |-  ( ph  ->  E. x ( ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360   A.wal 1550   E.wex 1551
This theorem is referenced by:  bnj1275  29247  bnj1340  29257  bnj594  29345  bnj1398  29465
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-ex 1552  df-nf 1555
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