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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 10662 | . . 3 ⊢ BOUNDED {𝑥, 𝑦} | |
2 | bdcsn 10661 | . . 3 ⊢ BOUNDED {𝑧} | |
3 | 1, 2 | bdcun 10653 | . 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧}) |
4 | df-tp 3406 | . 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧}) | |
5 | 3, 4 | bdceqir 10635 | 1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧} |
Colors of variables: wff set class |
Syntax hints: ∪ cun 2971 {csn 3398 {cpr 3399 {ctp 3400 BOUNDED wbdc 10631 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 ax-ext 2063 ax-bd0 10604 ax-bdor 10607 ax-bdeq 10611 ax-bdsb 10613 |
This theorem depends on definitions: df-bi 115 df-clab 2068 df-cleq 2074 df-clel 2077 df-un 2977 df-sn 3404 df-pr 3405 df-tp 3406 df-bdc 10632 |
This theorem is referenced by: (None) |
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