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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcsn | GIF version |
Description: The singleton of a setvar is bounded. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdcsn | ⊢ BOUNDED {𝑥} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bdeq 14956 | . . 3 ⊢ BOUNDED 𝑦 = 𝑥 | |
2 | 1 | bdcab 14985 | . 2 ⊢ BOUNDED {𝑦 ∣ 𝑦 = 𝑥} |
3 | df-sn 3613 | . 2 ⊢ {𝑥} = {𝑦 ∣ 𝑦 = 𝑥} | |
4 | 2, 3 | bdceqir 14980 | 1 ⊢ BOUNDED {𝑥} |
Colors of variables: wff set class |
Syntax hints: {cab 2175 {csn 3607 BOUNDED wbdc 14976 |
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-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 ax-ext 2171 ax-bd0 14949 ax-bdeq 14956 ax-bdsb 14958 |
This theorem depends on definitions: df-bi 117 df-clab 2176 df-cleq 2182 df-clel 2185 df-sn 3613 df-bdc 14977 |
This theorem is referenced by: bdcpr 15007 bdctp 15008 bdvsn 15010 bdcsuc 15016 |
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