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Theorem sneqrg 3533
 Description: Closed form of sneqr 3531. (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 3386 . . . 4
21eqeq1d 2048 . . 3
3 eqeq1 2046 . . 3
42, 3imbi12d 223 . 2
5 vex 2560 . . 3
65sneqr 3531 . 2
74, 6vtoclg 2613 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393  csn 3375 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-sn 3381 This theorem is referenced by:  sneqbg  3534
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