Theorem vsnid 3403

Description: A setvar variable is a member of its singleton (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
vsnid	|- x e. { x }

Proof of Theorem vsnid

Step	Hyp	Ref	Expression
1		vex 2560	. 2 |- x e. _V
2	1	snid 3402	1 |- x e. { x }

Syntax hints:   e. 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:  dtruex  4283  fnressn  5349  fressnfv  5350  findcard2d  6348  findcard2sd  6349  diffifi  6351  ac6sfi  6352