Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  r19.28zv Structured version   Unicode version

Theorem r19.28zv 3929
 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:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem r19.28zv
StepHypRef Expression
1 r19.3rzv 3927 . . 3
21anbi1d 704 . 2
3 r19.26 2994 . 2
42, 3syl6rbbr 264 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wne 2662  wral 2817  c0 3790 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-v 3120  df-dif 3484  df-nul 3791 This theorem is referenced by:  raaanv  3942  raltpd  4156  iinrab  4393  iindif2  4400  iinin2  4401  reusv2lem5  4658  reusv7OLD  4665  xpiindi  5144  fint  5770  ixpiin  7507  neips  19482  txflf  20375  dfpo2  29111  diaglbN  36253  dihglbcpreN  36498
 Copyright terms: Public domain W3C validator