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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 9275 | . . 3 ⊢ BOUNDED y = x | |
2 | 1 | bdcab 9304 | . 2 ⊢ BOUNDED {y ∣ y = x} |
3 | df-sn 3373 | . 2 ⊢ {x} = {y ∣ y = x} | |
4 | 2, 3 | bdceqir 9299 | 1 ⊢ BOUNDED {x} |
Colors of variables: wff set class |
Syntax hints: {cab 2023 {csn 3367 BOUNDED wbdc 9295 |
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-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-4 1397 ax-17 1416 ax-ial 1424 ax-ext 2019 ax-bd0 9268 ax-bdeq 9275 ax-bdsb 9277 |
This theorem depends on definitions: df-bi 110 df-clab 2024 df-cleq 2030 df-clel 2033 df-sn 3373 df-bdc 9296 |
This theorem is referenced by: bdcpr 9326 bdctp 9327 bdvsn 9329 bdcsuc 9335 |
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