Theorem vsnid 3665

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 ∈ {𝑥}

Proof of Theorem vsnid

Step	Hyp	Ref	Expression
1		vex 2775	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3664	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 2176  {csn 3633

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-sn 3639

This theorem is referenced by:  rext  4259  snnex  4495  dtruex  4607  fnressn  5770  fressnfv  5771  findcard2d  6988  findcard2sd  6989  diffifi  6991  ac6sfi  6995  fisseneq  7031  finomni  7242  cc2lem  7378  modfsummodlem1  11767  txdis  14749  txdis1cn  14750