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Theorem exan 1904
Description: Place a conjunct in the scope of an existential quantifier. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Jan-2018.)
Hypothesis
Ref Expression
exan.1  |-  ( E. x ph  /\  ps )
Assertion
Ref Expression
exan  |-  E. x
( ph  /\  ps )

Proof of Theorem exan
StepHypRef Expression
1 exan.1 . 2  |-  ( E. x ph  /\  ps )
21simpri 450 . . . 4  |-  ps
32nfth 1563 . . 3  |-  F/ x ps
4319.41 1901 . 2  |-  ( E. x ( ph  /\  ps )  <->  ( E. x ph  /\  ps ) )
51, 4mpbir 202 1  |-  E. x
( ph  /\  ps )
Colors of variables: wff set class
Syntax hints:    /\ wa 360   E.wex 1551
This theorem is referenced by:  bm1.3ii  4335  fnchoice  27678
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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