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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdeli | GIF version |
Description: Inference associated with bdel 9965. Its converse is bdelir 9967. (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 9965 | . 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ BOUNDED 𝑥 ∈ 𝐴 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1393 BOUNDED wbd 9932 BOUNDED wbdc 9960 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-4 1400 |
This theorem depends on definitions: df-bi 110 df-bdc 9961 |
This theorem is referenced by: bdph 9970 bdcrab 9972 bdnel 9974 bdccsb 9980 bdcdif 9981 bdcun 9982 bdcin 9983 bdss 9984 bdsnss 9993 bdciun 9998 bdciin 9999 bdinex1 10019 bj-uniex2 10036 bj-inf2vnlem3 10097 |
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