Theorem r19.27zv 3893

Description: Restricted quantifier version of Theorem 19.27 of [Margaris] p. 90. It is valid only when the domain of quantification is not empty. (Contributed by NM, 19-Aug-2004.)

Assertion

Ref	Expression
r19.27zv

Distinct variable groups:   ,   ,

Proof of Theorem r19.27zv

Step	Hyp	Ref	Expression
1		r19.3rzv 3887	. . 3
2	1	anbi2d 703	. 2
3		r19.26 2958	. 2
4	2, 3	syl6rbbr 264	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =/=wne 2648  A.wral 2800  c0 3751

This theorem is referenced by:  raaanv  3902  txflf  19978  dfso3  27832  dibglbN  35662

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2805  df-v 3083  df-dif 3445  df-nul 3752