Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  r19.9rzv Structured version   Unicode version

Theorem r19.9rzv 3723
 Description: Restricted quantification of wff not containing quantified variable. (Contributed by NM, 27-May-1998.)
Assertion
Ref Expression
r19.9rzv
Distinct variable groups:   ,   ,

Proof of Theorem r19.9rzv
StepHypRef Expression
1 r19.3rzv 3722 . . . 4
21bicomd 194 . . 3
32con2bid 321 . 2
4 dfrex2 2719 . 2
53, 4syl6bbr 256 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wne 2600  wral 2706  wrex 2707  c0 3629 This theorem is referenced by:  r19.45zv  3726  r19.36zv  3729  iunconst  4102  fconstfv  5955  dvdsr02  15762  voliune  24586  dya2iocuni  24634  filnetlem4  26411 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-v 2959  df-dif 3324  df-nul 3630
 Copyright terms: Public domain W3C validator