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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 7235 | . . 3 ⊢ (1...(𝑀 + 𝑁)) ∈ V | |
3 | 2 | pwex 5262 | . 2 ⊢ 𝒫 (1...(𝑀 + 𝑁)) ∈ V |
4 | 1, 3 | rabex2 5216 | 1 ⊢ 𝑂 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1543 ∈ wcel 2110 {crab 3058 Vcvv 3401 𝒫 cpw 4503 ‘cfv 6369 (class class class)co 7202 1c1 10713 + caddc 10715 ℕcn 11813 ...cfz 13078 ♯chash 13879 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2158 ax-12 2175 ax-ext 2706 ax-sep 5181 ax-nul 5188 ax-pow 5247 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-tru 1546 df-fal 1556 df-ex 1788 df-nf 1792 df-sb 2071 df-mo 2537 df-eu 2566 df-clab 2713 df-cleq 2726 df-clel 2812 df-ral 3059 df-rex 3060 df-rab 3063 df-v 3403 df-sbc 3688 df-dif 3860 df-un 3862 df-in 3864 df-ss 3874 df-nul 4228 df-pw 4505 df-sn 4532 df-pr 4534 df-uni 4810 df-iota 6327 df-fv 6377 df-ov 7205 |
This theorem is referenced by: ballotlem2 32139 ballotlem8 32187 |
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