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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 6577 | . . 3 ⊢ (1...(𝑀 + 𝑁)) ∈ V | |
3 | 2 | pwex 4774 | . 2 ⊢ 𝒫 (1...(𝑀 + 𝑁)) ∈ V |
4 | 1, 3 | rabex2 4742 | 1 ⊢ 𝑂 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∈ wcel 1977 {crab 2900 Vcvv 3173 𝒫 cpw 4108 ‘cfv 5804 (class class class)co 6549 1c1 9816 + caddc 9818 ℕcn 10897 ...cfz 12197 #chash 12979 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pow 4769 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-eu 2462 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ral 2901 df-rex 2902 df-rab 2905 df-v 3175 df-sbc 3403 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-pw 4110 df-sn 4126 df-pr 4128 df-uni 4373 df-iota 5768 df-fv 5812 df-ov 6552 |
This theorem is referenced by: ballotlem2 29877 ballotlem8 29925 |
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