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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 13036 | . 2 ⊢ BOUNDED 𝑦 ∈ {𝑥 ∣ 𝜑} |
3 | 2 | bdelir 13045 | 1 ⊢ BOUNDED {𝑥 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: {cab 2125 BOUNDED wbd 13010 BOUNDED wbdc 13038 |
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 1425 ax-bd0 13011 ax-bdsb 13020 |
This theorem depends on definitions: df-bi 116 df-clab 2126 df-bdc 13039 |
This theorem is referenced by: bds 13049 bdcrab 13050 bdccsb 13058 bdcdif 13059 bdcun 13060 bdcin 13061 bdcpw 13067 bdcsn 13068 bdcuni 13074 bdcint 13075 bdciun 13076 bdciin 13077 bdcriota 13081 bj-bdfindis 13145 |
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