Theorem 19.29r 1557

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 1556	. 2 |- ( ( A. x ps /\ E. x ph ) -> E. x ( ps /\ ph ) )
2		ancom 262	. 2 |- ( ( E. x ph /\ A. x ps ) <-> ( A. x ps /\ E. x ph ) )
3		exancom 1544	. 2 |- ( E. x ( ph /\ ps ) <-> E. x ( ps /\ ph ) )
4	1, 2, 3	3imtr4i 199	1 |- ( ( E. x ph /\ A. x ps ) -> E. x ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 102   A.wal 1287   E.wex 1426

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  19.29r2  1558  19.29x  1559  exan  1628  ax9o  1633  equvini  1688  eu2  1992  intab  3717  imadiflem  5093  bj-inex  11753