Theorem 19.29r 1645

Description: Variation of Theorem 19.29 of [Margaris] p. 90. (Contributed by NM, 18-Aug-1993.)

Assertion

Ref	Expression
19.29r	|- ( ( E. x ph /\ A. x ps ) -> E. x ( ph /\ ps ) )

Proof of Theorem 19.29r

Step	Hyp	Ref	Expression
1		19.29 1644	. 2 |- ( ( A. x ps /\ E. x ph ) -> E. x ( ps /\ ph ) )
2		ancom 266	. 2 |- ( ( E. x ph /\ A. x ps ) <-> ( A. x ps /\ E. x ph ) )
3		exancom 1632	. 2 |- ( E. x ( ph /\ ps ) <-> E. x ( ps /\ ph ) )
4	1, 2, 3	3imtr4i 201	1 |- ( ( E. x ph /\ A. x ps ) -> E. x ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 104   A.wal 1371   E.wex 1516

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-ial 1558

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.29r2  1646  19.29x  1647  exan  1717  ax9o  1722  equvini  1782  eu2  2100  intab  3928  imadiflem  5372  bj-inex  16042