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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdelir | GIF version |
Description: Inference associated with df-bdc 11732. Its converse is bdeli 11737. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdelir.1 | ⊢ BOUNDED 𝑥 ∈ 𝐴 |
Ref | Expression |
---|---|
bdelir | ⊢ BOUNDED 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-bdc 11732 | . 2 ⊢ (BOUNDED 𝐴 ↔ ∀𝑥BOUNDED 𝑥 ∈ 𝐴) | |
2 | bdelir.1 | . 2 ⊢ BOUNDED 𝑥 ∈ 𝐴 | |
3 | 1, 2 | mpgbir 1387 | 1 ⊢ BOUNDED 𝐴 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1438 BOUNDED wbd 11703 BOUNDED wbdc 11731 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-gen 1383 |
This theorem depends on definitions: df-bi 115 df-bdc 11732 |
This theorem is referenced by: bdcv 11739 bdcab 11740 bdcvv 11748 bdcnul 11756 bdop 11766 |
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