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Theorem ballotlemoex 34466
Description: 𝑂 is a set. (Contributed by Thierry Arnoux, 7-Dec-2016.)
Hypotheses
Ref Expression
ballotth.m 𝑀 ∈ ℕ
ballotth.n 𝑁 ∈ ℕ
ballotth.o 𝑂 = {𝑐 ∈ 𝒫 (1...(𝑀 + 𝑁)) ∣ (♯‘𝑐) = 𝑀}
Assertion
Ref Expression
ballotlemoex 𝑂 ∈ V
Distinct variable groups:   𝑀,𝑐   𝑁,𝑐   𝑂,𝑐

Proof of Theorem ballotlemoex
StepHypRef Expression
1 ballotth.o . 2 𝑂 = {𝑐 ∈ 𝒫 (1...(𝑀 + 𝑁)) ∣ (♯‘𝑐) = 𝑀}
2 ovex 7463 . . 3 (1...(𝑀 + 𝑁)) ∈ V
32pwex 5385 . 2 𝒫 (1...(𝑀 + 𝑁)) ∈ V
41, 3rabex2 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  cn 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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