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Theorem 19.40 1522
Description: Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.40  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )

Proof of Theorem 19.40
StepHypRef Expression
1 exsimpl 1508 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
2 simpr 103 . . 3  |-  ( (
ph  /\  ps )  ->  ps )
32eximi 1491 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
41, 3jca 290 1  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97   E.wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  19.40-2  1523  19.41h  1575  19.41  1576  exdistrfor  1681  uniin  3600  copsexg  3981  dmin  4543  imadif  4979  imainlem  4980
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