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Theorem exan 1978
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 460 . . . 4  |-  ps
32nfth 1630 . . 3  |-  F/ x ps
4319.41 1976 . 2  |-  ( E. x ( ph  /\  ps )  <->  ( E. x ph  /\  ps ) )
51, 4mpbir 209 1  |-  E. x
( ph  /\  ps )
Colors of variables: wff setvar class
Syntax hints:    /\ wa 367   E.wex 1617
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-ex 1618  df-nf 1622
This theorem is referenced by:  bm1.3ii  4563  ac6s6f  30824  fnchoice  31647
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