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Theorem ballotlemoex 31642
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 7178 . . 3 (1...(𝑀 + 𝑁)) ∈ V
32pwex 5272 . 2 𝒫 (1...(𝑀 + 𝑁)) ∈ V
41, 3rabex2 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  cn 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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