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Theorem 19.40-2 1597
Description: Theorem *11.42 in [WhiteheadRussell] p. 163. Theorem 19.40 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
19.40-2  |-  ( E. x E. y (
ph  /\  ps )  ->  ( E. x E. y ph  /\  E. x E. y ps ) )

Proof of Theorem 19.40-2
StepHypRef Expression
1 19.40 1596 . . 3  |-  ( E. y ( ph  /\  ps )  ->  ( E. y ph  /\  E. y ps ) )
21eximi 1563 . 2  |-  ( E. x E. y (
ph  /\  ps )  ->  E. x ( E. y ph  /\  E. y ps ) )
3 19.40 1596 . 2  |-  ( E. x ( E. y ph  /\  E. y ps )  ->  ( E. x E. y ph  /\  E. x E. y ps ) )
42, 3syl 15 1  |-  ( E. x E. y (
ph  /\  ps )  ->  ( E. x E. y ph  /\  E. x E. y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   E.wex 1528
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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