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Theorem sneqrg 4201
 Description: Closed form of sneqr 4199. (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 4042 . . . 4
21eqeq1d 2459 . . 3
3 eqeq1 2461 . . 3
42, 3imbi12d 320 . 2
5 vex 3112 . . 3
65sneqr 4199 . 2
74, 6vtoclg 3167 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1395   wcel 1819  csn 4032 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sn 4033 This theorem is referenced by:  sneqbg  4202  altopth1  29777  altopth2  29778
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