Theorem r19.27zv 3756

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 3750	. . 3
2	1	anbi2d 688	. 2
3		r19.26 2828	. 2
4	2, 3	syl6rbbr 258	1

Syntax hints:  ->wi 4  <->wb 178  /\wa 362  =/=wne 2585  A.wral 2694  c0 3614

This theorem is referenced by:  raaanv  3765  txflf  19283  dfso3  27078  dibglbN  34248

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1586  ax-4 1597  ax-5 1661  ax-6 1701  ax-7 1721  ax-10 1768  ax-11 1773  ax-12 1785  ax-13 1934  ax-ext 2403

This theorem depends on definitions:  df-bi 179  df-or 363  df-an 364  df-tru 1355  df-ex 1582  df-nf 1585  df-sb 1694  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2547  df-ne 2587  df-ral 2699  df-v 2953  df-dif 3308  df-nul 3615