![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > Mathboxes > bdssexi | GIF version |
Description: Bounded version of ssexi 3977. (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 11793 | . 2 ⊢ (𝐴 ⊆ 𝐵 → 𝐴 ∈ V) |
5 | 1, 4 | ax-mp 7 | 1 ⊢ 𝐴 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1438 Vcvv 2619 ⊆ wss 2999 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-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-bdsep 11775 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-in 3005 df-ss 3012 df-bdc 11732 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |