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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 2740 | . 2 ⊢ 𝑥 ∈ V | |
2 | 1 | snid 3622 | 1 ⊢ 𝑥 ∈ {𝑥} |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2148 {csn 3591 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-sn 3597 |
This theorem is referenced by: rext 4211 snnex 4444 dtruex 4554 fnressn 5697 fressnfv 5698 findcard2d 6884 findcard2sd 6885 diffifi 6887 ac6sfi 6891 fisseneq 6924 finomni 7131 cc2lem 7243 modfsummodlem1 11435 txdis 13410 txdis1cn 13411 |
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