![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-uniex | GIF version |
Description: uniex 4264 from bounded separation. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-uniex.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
bj-uniex | ⊢ ∪ 𝐴 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-uniex.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | unieq 3662 | . . 3 ⊢ (𝑥 = 𝐴 → ∪ 𝑥 = ∪ 𝐴) | |
3 | 2 | eleq1d 2156 | . 2 ⊢ (𝑥 = 𝐴 → (∪ 𝑥 ∈ V ↔ ∪ 𝐴 ∈ V)) |
4 | bj-uniex2 11807 | . . 3 ⊢ ∃𝑦 𝑦 = ∪ 𝑥 | |
5 | 4 | issetri 2628 | . 2 ⊢ ∪ 𝑥 ∈ V |
6 | 1, 3, 5 | vtocl 2673 | 1 ⊢ ∪ 𝐴 ∈ V |
Colors of variables: wff set class |
Syntax hints: = wceq 1289 ∈ wcel 1438 Vcvv 2619 ∪ cuni 3653 |
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-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-un 4260 ax-bd0 11704 ax-bdex 11710 ax-bdel 11712 ax-bdsb 11713 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-rex 2365 df-v 2621 df-uni 3654 df-bdc 11732 |
This theorem is referenced by: bj-uniexg 11809 bj-unex 11810 |
Copyright terms: Public domain | W3C validator |