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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdssexi | GIF version |
Description: Bounded version of ssexi 4156. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bdssexi.bd | ⊢ BOUNDED 𝐴 |
bdssexi.1 | ⊢ 𝐵 ∈ V |
bdssexi.2 | ⊢ 𝐴 ⊆ 𝐵 |
Ref | Expression |
---|---|
bdssexi | ⊢ 𝐴 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdssexi.2 | . 2 ⊢ 𝐴 ⊆ 𝐵 | |
2 | bdssexi.bd | . . 3 ⊢ BOUNDED 𝐴 | |
3 | bdssexi.1 | . . 3 ⊢ 𝐵 ∈ V | |
4 | 2, 3 | bdssex 15115 | . 2 ⊢ (𝐴 ⊆ 𝐵 → 𝐴 ∈ V) |
5 | 1, 4 | ax-mp 5 | 1 ⊢ 𝐴 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 Vcvv 2752 ⊆ wss 3144 BOUNDED wbdc 15053 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-bdsep 15097 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-in 3150 df-ss 3157 df-bdc 15054 |
This theorem is referenced by: (None) |
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