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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdinex2 | GIF version |
Description: Bounded version of inex2 4099. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bdinex2.bd | ⊢ BOUNDED 𝐵 |
bdinex2.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
bdinex2 | ⊢ (𝐵 ∩ 𝐴) ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | incom 3299 | . 2 ⊢ (𝐵 ∩ 𝐴) = (𝐴 ∩ 𝐵) | |
2 | bdinex2.bd | . . 3 ⊢ BOUNDED 𝐵 | |
3 | bdinex2.1 | . . 3 ⊢ 𝐴 ∈ V | |
4 | 2, 3 | bdinex1 13485 | . 2 ⊢ (𝐴 ∩ 𝐵) ∈ V |
5 | 1, 4 | eqeltri 2230 | 1 ⊢ (𝐵 ∩ 𝐴) ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2128 Vcvv 2712 ∩ cin 3101 BOUNDED wbdc 13426 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-bdsep 13470 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-in 3108 df-bdc 13427 |
This theorem is referenced by: bdssex 13488 |
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