Theorem 19.29r 1802

Description: Variation of 19.29 1801. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Nov-2020.)

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		pm3.21 464	. . 3 |- ( ps -> ( ph -> ( ph /\ ps ) ) )
2	1	aleximi 1759	. 2 |- ( A. x ps -> ( E. x ph -> E. x ( ph /\ ps ) ) )
3	2	impcom 446	1 |- ( ( E. x ph /\ A. 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:  19.29r2  1803  19.29x  1804  intab  4507  imadif  5973  kmlem6  8977  2ndcdisj  21259  fmcncfil  29977  bnj907  31035  bj-19.41al  32637