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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcpr | GIF version |
Description: The pair of two setvars is bounded. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdcpr | ⊢ BOUNDED {𝑥, 𝑦} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcsn 15080 | . . 3 ⊢ BOUNDED {𝑥} | |
2 | bdcsn 15080 | . . 3 ⊢ BOUNDED {𝑦} | |
3 | 1, 2 | bdcun 15072 | . 2 ⊢ BOUNDED ({𝑥} ∪ {𝑦}) |
4 | df-pr 3614 | . 2 ⊢ {𝑥, 𝑦} = ({𝑥} ∪ {𝑦}) | |
5 | 3, 4 | bdceqir 15054 | 1 ⊢ BOUNDED {𝑥, 𝑦} |
Colors of variables: wff set class |
Syntax hints: ∪ cun 3142 {csn 3607 {cpr 3608 BOUNDED wbdc 15050 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 ax-ext 2171 ax-bd0 15023 ax-bdor 15026 ax-bdeq 15030 ax-bdsb 15032 |
This theorem depends on definitions: df-bi 117 df-clab 2176 df-cleq 2182 df-clel 2185 df-un 3148 df-sn 3613 df-pr 3614 df-bdc 15051 |
This theorem is referenced by: bdctp 15082 bdop 15085 |
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