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Theorem 19.40 1567
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 1553 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
2 simpr 108 . . 3  |-  ( (
ph  /\  ps )  ->  ps )
32eximi 1536 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
41, 3jca 300 1  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   E.wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  19.40-2  1568  19.41h  1620  19.41  1621  exdistrfor  1728  uniin  3668  copsexg  4062  dmin  4632  imadif  5080  imainlem  5081
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