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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdeli | GIF version |
Description: Inference associated with bdel 12970. Its converse is bdelir 12972. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdeli.1 | ⊢ BOUNDED 𝐴 |
Ref | Expression |
---|---|
bdeli | ⊢ BOUNDED 𝑥 ∈ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdeli.1 | . 2 ⊢ BOUNDED 𝐴 | |
2 | bdel 12970 | . 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ BOUNDED 𝑥 ∈ 𝐴 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 BOUNDED wbd 12937 BOUNDED wbdc 12965 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-4 1472 |
This theorem depends on definitions: df-bi 116 df-bdc 12966 |
This theorem is referenced by: bdph 12975 bdcrab 12977 bdnel 12979 bdccsb 12985 bdcdif 12986 bdcun 12987 bdcin 12988 bdss 12989 bdsnss 12998 bdciun 13003 bdciin 13004 bdinex1 13024 bj-uniex2 13041 bj-inf2vnlem3 13097 |
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