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Mathbox for Thierry Arnoux |
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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 7463 | . . 3 ⊢ (1...(𝑀 + 𝑁)) ∈ V | |
3 | 2 | pwex 5385 | . 2 ⊢ 𝒫 (1...(𝑀 + 𝑁)) ∈ V |
4 | 1, 3 | rabex2 5346 | 1 ⊢ 𝑂 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1536 ∈ wcel 2105 {crab 3432 Vcvv 3477 𝒫 cpw 4604 ‘cfv 6562 (class class class)co 7430 1c1 11153 + caddc 11155 ℕcn 12263 ...cfz 13543 ♯chash 14365 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 ax-sep 5301 ax-nul 5311 ax-pow 5370 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1539 df-fal 1549 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-ne 2938 df-rab 3433 df-v 3479 df-dif 3965 df-un 3967 df-in 3969 df-ss 3979 df-nul 4339 df-pw 4606 df-sn 4631 df-pr 4633 df-uni 4912 df-iota 6515 df-fv 6570 df-ov 7433 |
This theorem is referenced by: ballotlem2 34469 ballotlem8 34517 |
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