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Mirrors > Home > ILE Home > Th. List > vsnid | GIF version |
Description: A setvar variable is a member of its singleton (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
vsnid | ⊢ 𝑥 ∈ {𝑥} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2715 | . 2 ⊢ 𝑥 ∈ V | |
2 | 1 | snid 3591 | 1 ⊢ 𝑥 ∈ {𝑥} |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2128 {csn 3560 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-sn 3566 |
This theorem is referenced by: rext 4176 snnex 4409 dtruex 4519 fnressn 5654 fressnfv 5655 findcard2d 6837 findcard2sd 6838 diffifi 6840 ac6sfi 6844 fisseneq 6877 finomni 7084 cc2lem 7187 modfsummodlem1 11357 txdis 12719 txdis1cn 12720 |
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