Theorem 19.27v 1908

Description: Version of 19.27 2095 with a dv condition, requiring fewer axioms. (Contributed by NM, 3-Jun-2004.)

Assertion

Ref	Expression
19.27v	|- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ ps ) )

Distinct variable group:   ps, x

Allowed substitution hint:   ph( x)

Proof of Theorem 19.27v

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 ps <-> ps )
3	2	anbi2i 730	. 2 |- ( ( A. x ph /\ A. x ps ) <-> ( A. x ph /\ ps ) )
4	1, 3	bitri 264	1 |- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ 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:  rexrsb  41169