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

Theorem sneqrg 3968
 Description: Closed form of sneqr 3966. (Contributed by Scott Fenton, 1-Apr-2011.)
Assertion
Ref Expression
sneqrg

Proof of Theorem sneqrg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sneq 3825 . . . 4
21eqeq1d 2444 . . 3
3 eqeq1 2442 . . 3
42, 3imbi12d 312 . 2
5 vex 2959 . . 3
65sneqr 3966 . 2
74, 6vtoclg 3011 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  csn 3814 This theorem is referenced by:  sneqbg  3969  altopth1  25810  altopth2  25811 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sn 3820
 Copyright terms: Public domain W3C validator