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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 7178 | . . 3 ⊢ (1...(𝑀 + 𝑁)) ∈ V | |
3 | 2 | pwex 5272 | . 2 ⊢ 𝒫 (1...(𝑀 + 𝑁)) ∈ V |
4 | 1, 3 | rabex2 5228 | 1 ⊢ 𝑂 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ∈ wcel 2105 {crab 3139 Vcvv 3492 𝒫 cpw 4535 ‘cfv 6348 (class class class)co 7145 1c1 10526 + caddc 10528 ℕcn 11626 ...cfz 12880 ♯chash 13678 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pow 5257 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ral 3140 df-rex 3141 df-rab 3144 df-v 3494 df-sbc 3770 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-pw 4537 df-sn 4558 df-pr 4560 df-uni 4831 df-iota 6307 df-fv 6356 df-ov 7148 |
This theorem is referenced by: ballotlem2 31645 ballotlem8 31693 |
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