Theorem r19.27zv 3929

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 3922	. . 3
2	1	anbi2d 703	. 2
3		r19.26 2984	. 2
4	2, 3	syl6rbbr 264	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =/=wne 2652  A.wral 2807  c0 3784

This theorem is referenced by:  raaanv  3938  txflf  20507  dfso3  29097  dibglbN  36893

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-v 3111  df-dif 3478  df-nul 3785