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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdctp | GIF version |
Description: The unordered triple of three setvars is bounded. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdctp | ⊢ BOUNDED {𝑥, 𝑦, 𝑧} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcpr 13594 | . . 3 ⊢ BOUNDED {𝑥, 𝑦} | |
2 | bdcsn 13593 | . . 3 ⊢ BOUNDED {𝑧} | |
3 | 1, 2 | bdcun 13585 | . 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧}) |
4 | df-tp 3578 | . 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧}) | |
5 | 3, 4 | bdceqir 13567 | 1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧} |
Colors of variables: wff set class |
Syntax hints: ∪ cun 3109 {csn 3570 {cpr 3571 {ctp 3572 BOUNDED wbdc 13563 |
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-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-17 1513 ax-ial 1521 ax-ext 2146 ax-bd0 13536 ax-bdor 13539 ax-bdeq 13543 ax-bdsb 13545 |
This theorem depends on definitions: df-bi 116 df-clab 2151 df-cleq 2157 df-clel 2160 df-un 3115 df-sn 3576 df-pr 3577 df-tp 3578 df-bdc 13564 |
This theorem is referenced by: (None) |
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