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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 9991 | . . 3 ⊢ BOUNDED {𝑥, 𝑦} | |
2 | bdcsn 9990 | . . 3 ⊢ BOUNDED {𝑧} | |
3 | 1, 2 | bdcun 9982 | . 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧}) |
4 | df-tp 3383 | . 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧}) | |
5 | 3, 4 | bdceqir 9964 | 1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧} |
Colors of variables: wff set class |
Syntax hints: ∪ cun 2915 {csn 3375 {cpr 3376 {ctp 3377 BOUNDED wbdc 9960 |
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 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 ax-bd0 9933 ax-bdor 9936 ax-bdeq 9940 ax-bdsb 9942 |
This theorem depends on definitions: df-bi 110 df-clab 2027 df-cleq 2033 df-clel 2036 df-un 2922 df-sn 3381 df-pr 3382 df-tp 3383 df-bdc 9961 |
This theorem is referenced by: (None) |
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