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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcab | GIF version |
Description: A class defined by class abstraction using a bounded formula is bounded. (Contributed by BJ, 6-Oct-2019.) |
Ref | Expression |
---|---|
bdcab.1 | ⊢ BOUNDED 𝜑 |
Ref | Expression |
---|---|
bdcab | ⊢ BOUNDED {𝑥 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcab.1 | . . 3 ⊢ BOUNDED 𝜑 | |
2 | 1 | bdab 13838 | . 2 ⊢ BOUNDED 𝑦 ∈ {𝑥 ∣ 𝜑} |
3 | 2 | bdelir 13847 | 1 ⊢ BOUNDED {𝑥 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: {cab 2156 BOUNDED wbd 13812 BOUNDED wbdc 13840 |
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-gen 1442 ax-bd0 13813 ax-bdsb 13822 |
This theorem depends on definitions: df-bi 116 df-clab 2157 df-bdc 13841 |
This theorem is referenced by: bds 13851 bdcrab 13852 bdccsb 13860 bdcdif 13861 bdcun 13862 bdcin 13863 bdcpw 13869 bdcsn 13870 bdcuni 13876 bdcint 13877 bdciun 13878 bdciin 13879 bdcriota 13883 bj-bdfindis 13947 |
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