Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  r19.36zv Unicode version

Theorem r19.36zv 3664
 Description: Restricted quantifier version of Theorem 19.36 of [Margaris] p. 90. It is valid only when the domain of quantification is not empty. (Contributed by NM, 20-Sep-2003.)
Assertion
Ref Expression
r19.36zv
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem r19.36zv
StepHypRef Expression
1 r19.9rzv 3658 . . 3
21imbi2d 308 . 2
3 r19.35 2791 . 2
42, 3syl6rbbr 256 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wne 2543  wral 2642  wrex 2643  c0 3564 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rex 2648  df-v 2894  df-dif 3259  df-nul 3565
 Copyright terms: Public domain W3C validator