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Theorem 19.29 1688
Description: Theorem 19.29 of [Margaris] p. 90. See also 19.29r 1689. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
19.29  |-  ( ( A. x ph  /\  E. x ps )  ->  E. x ( ph  /\  ps ) )

Proof of Theorem 19.29
StepHypRef Expression
1 pm3.2 445 . . 3  |-  ( ph  ->  ( ps  ->  ( ph  /\  ps ) ) )
21aleximi 1658 . 2  |-  ( A. x ph  ->  ( E. x ps  ->  E. x
( ph  /\  ps )
) )
32imp 427 1  |-  ( ( A. x ph  /\  E. x ps )  ->  E. x ( ph  /\  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367   A.wal 1396   E.wex 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618
This theorem is referenced by:  19.29r  1689  19.29x  1691  19.40b  1703  supsrlem  9477  1stccnp  20129  iscmet3  21898  isch3  26357  stoweidlem35  32056  bnj849  34384
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