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| Mirrors > Home > MPE Home > Th. List > Mathboxes > ballotlemoex | Structured version Visualization version GIF version | ||
| Description: 𝑂 is a set. (Contributed by Thierry Arnoux, 7-Dec-2016.) |
| Ref | Expression |
|---|---|
| ballotth.m | ⊢ 𝑀 ∈ ℕ |
| ballotth.n | ⊢ 𝑁 ∈ ℕ |
| ballotth.o | ⊢ 𝑂 = {𝑐 ∈ 𝒫 (1...(𝑀 + 𝑁)) ∣ (♯‘𝑐) = 𝑀} |
| Ref | Expression |
|---|---|
| ballotlemoex | ⊢ 𝑂 ∈ V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ballotth.o | . 2 ⊢ 𝑂 = {𝑐 ∈ 𝒫 (1...(𝑀 + 𝑁)) ∣ (♯‘𝑐) = 𝑀} | |
| 2 | ovex 7464 | . . 3 ⊢ (1...(𝑀 + 𝑁)) ∈ V | |
| 3 | 2 | pwex 5380 | . 2 ⊢ 𝒫 (1...(𝑀 + 𝑁)) ∈ V |
| 4 | 1, 3 | rabex2 5341 | 1 ⊢ 𝑂 ∈ V |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ∈ wcel 2108 {crab 3436 Vcvv 3480 𝒫 cpw 4600 ‘cfv 6561 (class class class)co 7431 1c1 11156 + caddc 11158 ℕcn 12266 ...cfz 13547 ♯chash 14369 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pow 5365 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-ne 2941 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-in 3958 df-ss 3968 df-nul 4334 df-pw 4602 df-sn 4627 df-pr 4629 df-uni 4908 df-iota 6514 df-fv 6569 df-ov 7434 |
| This theorem is referenced by: ballotlem2 34491 ballotlem8 34539 |
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