Theorem 19.28v 1909

Description: Version of 19.28 2096 with a dv condition, requiring fewer axioms. (Contributed by NM, 25-Mar-2004.)

Assertion

Ref	Expression
19.28v	|- ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem 19.28v

Step	Hyp	Ref	Expression
1		19.26 1798	. 2 |- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ A. x ps ) )
2		19.3v 1897	. . 3 |- ( A. x ph <-> ph )
3	2	anbi1i 731	. 2 |- ( ( A. x ph /\ A. x ps ) <-> ( ph /\ A. x ps ) )
4	1, 3	bitri 264	1 |- ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )

Syntax hints:   <-> wb 196   /\ wa 384   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  reu6  3395  dfer2  7743  kmlem14  8985  kmlem15  8986  bnj1176  31073  bnj1186  31075  19.28vv  38585