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Theorem ballotlemoex 30877
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 6842 . . 3 (1...(𝑀 + 𝑁)) ∈ V
32pwex 4997 . 2 𝒫 (1...(𝑀 + 𝑁)) ∈ V
41, 3rabex2 4966 1 𝑂 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1632  wcel 2139  {crab 3054  Vcvv 3340  𝒫 cpw 4302  cfv 6049  (class class class)co 6814  1c1 10149   + caddc 10151  cn 11232  ...cfz 12539  chash 13331
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933  ax-nul 4941  ax-pow 4992
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-eu 2611  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-ral 3055  df-rex 3056  df-rab 3059  df-v 3342  df-sbc 3577  df-dif 3718  df-un 3720  df-in 3722  df-ss 3729  df-nul 4059  df-pw 4304  df-sn 4322  df-pr 4324  df-uni 4589  df-iota 6012  df-fv 6057  df-ov 6817
This theorem is referenced by:  ballotlem2  30880  ballotlem8  30928
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