Theorem 19.29r 1609

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 1608	. 2 |- ( ( A. x ps /\ E. x ph ) -> E. x ( ps /\ ph ) )
2		ancom 264	. 2 |- ( ( E. x ph /\ A. x ps ) <-> ( A. x ps /\ E. x ph ) )
3		exancom 1596	. 2 |- ( E. x ( ph /\ ps ) <-> E. x ( ps /\ ph ) )
4	1, 2, 3	3imtr4i 200	1 |- ( ( E. x ph /\ A. x ps ) -> E. x ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 103   A.wal 1341   E.wex 1480

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-ial 1522

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.29r2  1610  19.29x  1611  exan  1681  ax9o  1686  equvini  1746  eu2  2058  intab  3853  imadiflem  5267  bj-inex  13789