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Theorem ballotlemoex 29711
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 6453 . . 3 (1...(𝑀 + 𝑁)) ∈ V
32pwex 4673 . 2 𝒫 (1...(𝑀 + 𝑁)) ∈ V
41, 3rabex2 4641 1 𝑂 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  wcel 1938  {crab 2804  Vcvv 3077  𝒫 cpw 4011  cfv 5689  (class class class)co 6425  1c1 9690   + caddc 9692  cn 10773  ...cfz 12062  #chash 12844
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-5 1793  ax-6 1838  ax-7 1885  ax-9 1947  ax-10 1966  ax-11 1971  ax-12 1983  ax-13 2137  ax-ext 2494  ax-sep 4607  ax-nul 4616  ax-pow 4668
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1699  df-sb 1831  df-eu 2366  df-clab 2501  df-cleq 2507  df-clel 2510  df-nfc 2644  df-ral 2805  df-rex 2806  df-rab 2809  df-v 3079  df-sbc 3307  df-dif 3447  df-un 3449  df-in 3451  df-ss 3458  df-nul 3778  df-pw 4013  df-sn 4029  df-pr 4031  df-uni 4271  df-iota 5653  df-fv 5697  df-ov 6428
This theorem is referenced by:  ballotlem2  29714  ballotlem8  29762  ballotlem8OLD  29800
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