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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 11119 | . . 3 ⊢ BOUNDED {𝑥, 𝑦} | |
2 | bdcsn 11118 | . . 3 ⊢ BOUNDED {𝑧} | |
3 | 1, 2 | bdcun 11110 | . 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧}) |
4 | df-tp 3433 | . 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧}) | |
5 | 3, 4 | bdceqir 11092 | 1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧} |
Colors of variables: wff set class |
Syntax hints: ∪ cun 2984 {csn 3425 {cpr 3426 {ctp 3427 BOUNDED wbdc 11088 |
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 1379 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-4 1443 ax-17 1462 ax-ial 1470 ax-ext 2067 ax-bd0 11061 ax-bdor 11064 ax-bdeq 11068 ax-bdsb 11070 |
This theorem depends on definitions: df-bi 115 df-clab 2072 df-cleq 2078 df-clel 2081 df-un 2990 df-sn 3431 df-pr 3432 df-tp 3433 df-bdc 11089 |
This theorem is referenced by: (None) |
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