Theorem 19.29 1801

Description: Theorem 19.29 of [Margaris] p. 90. See also 19.29r 1802. (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

Step	Hyp	Ref	Expression
1		pm3.2 463	. . 3 |- ( ph -> ( ps -> ( ph /\ ps ) ) )
2	1	aleximi 1759	. 2 |- ( A. x ph -> ( E. x ps -> E. x ( ph /\ ps ) ) )
3	2	imp 445	1 |- ( ( A. x ph /\ E. x ps ) -> E. x ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 384   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  19.29x  1804  supsrlem  9932  1stccnp  21265  iscmet3  23091  isch3  28098  bnj849  30995  axc11n11r  32673  stoweidlem35  40252