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Theorem ballotlemoex 31851
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 7172 . . 3 (1...(𝑀 + 𝑁)) ∈ V
32pwex 5249 . 2 𝒫 (1...(𝑀 + 𝑁)) ∈ V
41, 3rabex2 5204 1 𝑂 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  wcel 2112  {crab 3113  Vcvv 3444  𝒫 cpw 4500  cfv 6328  (class class class)co 7139  1c1 10531   + caddc 10533  cn 11629  ...cfz 12889  chash 13690
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773  ax-sep 5170  ax-nul 5177  ax-pow 5234
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2601  df-eu 2632  df-clab 2780  df-cleq 2794  df-clel 2873  df-ral 3114  df-rex 3115  df-rab 3118  df-v 3446  df-sbc 3724  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4247  df-pw 4502  df-sn 4529  df-pr 4531  df-uni 4804  df-iota 6287  df-fv 6336  df-ov 7142
This theorem is referenced by:  ballotlem2  31854  ballotlem8  31902
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