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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-bdcel | GIF version |
Description: Boundedness of a membership formula. (Contributed by BJ, 8-Dec-2019.) |
Ref | Expression |
---|---|
bj-bdcel.bd | ⊢ BOUNDED 𝑦 = 𝐴 |
Ref | Expression |
---|---|
bj-bdcel | ⊢ BOUNDED 𝐴 ∈ 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-bdcel.bd | . . 3 ⊢ BOUNDED 𝑦 = 𝐴 | |
2 | 1 | ax-bdex 14541 | . 2 ⊢ BOUNDED ∃𝑦 ∈ 𝑥 𝑦 = 𝐴 |
3 | risset 2505 | . 2 ⊢ (𝐴 ∈ 𝑥 ↔ ∃𝑦 ∈ 𝑥 𝑦 = 𝐴) | |
4 | 2, 3 | bd0r 14547 | 1 ⊢ BOUNDED 𝐴 ∈ 𝑥 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 ∈ wcel 2148 ∃wrex 2456 BOUNDED wbd 14534 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-ial 1534 ax-bd0 14535 ax-bdex 14541 |
This theorem depends on definitions: df-bi 117 df-clel 2173 df-rex 2461 |
This theorem is referenced by: bj-bd0el 14590 bj-bdsucel 14604 |
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