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Theorem exintr 1750
Description: Introduce a conjunct in the scope of an existential quantifier. (Contributed by NM, 11-Aug-1993.)
Assertion
Ref Expression
exintr  |-  ( A. x ( ph  ->  ps )  ->  ( E. x ph  ->  E. x
( ph  /\  ps )
) )

Proof of Theorem exintr
StepHypRef Expression
1 exintrbi 1748 . 2  |-  ( A. x ( ph  ->  ps )  ->  ( E. x ph  <->  E. x ( ph  /\ 
ps ) ) )
21biimpd 210 1  |-  ( A. x ( ph  ->  ps )  ->  ( E. x ph  ->  E. x
( ph  /\  ps )
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370   A.wal 1435   E.wex 1657
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658
This theorem is referenced by:  equs4v  1839  equs4  2092  eupickbi  2338  ceqsex  3117  r19.2z  3888  pwpw0  4148  pwsnALT  4214  bnj1023  29600  bnj1109  29606  ceqsex3OLD  32400  pm10.55  36688
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