Theorem 19.29r 1644

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 1643	. 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 1631	. 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 1515

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-ial 1557

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.29r2  1645  19.29x  1646  exan  1716  ax9o  1721  equvini  1781  eu2  2098  intab  3914  imadiflem  5353  bj-inex  15843