Theorem r19.28zv 3924

Description: Restricted quantifier version of Theorem 19.28 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
r19.28zv

Distinct variable groups:   ,   ,

Proof of Theorem r19.28zv

Step	Hyp	Ref	Expression
1		r19.3rzv 3922	. . 3
2	1	anbi1d 704	. 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  raltpd  4153  iinrab  4392  iindif2  4399  iinin2  4400  reusv2lem5  4657  reusv7OLD  4664  xpiindi  5143  fint  5769  ixpiin  7515  neips  19614  txflf  20507  dfpo2  29184  diaglbN  36782  dihglbcpreN  37027

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