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Theorem exintr 1602
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 1601 . 2  |-  ( A. x ( ph  ->  ps )  ->  ( E. x ph  <->  E. x ( ph  /\ 
ps ) ) )
21biimpd 200 1  |-  ( A. x ( ph  ->  ps )  ->  ( E. x ph  ->  E. x
( ph  /\  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    /\ wa 360   A.wal 1528   E.wex 1529
This theorem is referenced by:  ceqsex  2823  r19.2z  3544  pwpw0  3764  pwsnALT  3823  ceqsex3OLD  26125  pm10.55  26963  bnj1023  28079  bnj1109  28085
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1530
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