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Theorem ballotlemoex 24515
Description:  O is a set. (Contributed by Thierry Arnoux, 7-Dec-2016.)
Hypotheses
Ref Expression
ballotth.m  |-  M  e.  NN
ballotth.n  |-  N  e.  NN
ballotth.o  |-  O  =  { c  e.  ~P ( 1 ... ( M  +  N )
)  |  ( # `  c )  =  M }
Assertion
Ref Expression
ballotlemoex  |-  O  e. 
_V
Distinct variable groups:    M, c    N, c    O, c

Proof of Theorem ballotlemoex
StepHypRef Expression
1 ovex 6038 . . 3  |-  ( 1 ... ( M  +  N ) )  e. 
_V
21pwex 4316 . 2  |-  ~P (
1 ... ( M  +  N ) )  e. 
_V
3 ballotth.o . . 3  |-  O  =  { c  e.  ~P ( 1 ... ( M  +  N )
)  |  ( # `  c )  =  M }
4 ssrab2 3364 . . 3  |-  { c  e.  ~P ( 1 ... ( M  +  N ) )  |  ( # `  c
)  =  M }  C_ 
~P ( 1 ... ( M  +  N
) )
53, 4eqsstri 3314 . 2  |-  O  C_  ~P ( 1 ... ( M  +  N )
)
62, 5ssexi 4282 1  |-  O  e. 
_V
Colors of variables: wff set class
Syntax hints:    = wceq 1649    e. wcel 1717   {crab 2646   _Vcvv 2892   ~Pcpw 3735   ` cfv 5387  (class class class)co 6013   1c1 8917    + caddc 8919   NNcn 9925   ...cfz 10968   #chash 11538
This theorem is referenced by:  ballotlem2  24518  ballotlem8  24566
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361  ax-sep 4264  ax-nul 4272  ax-pow 4311
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2235  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-sbc 3098  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-pw 3737  df-sn 3756  df-pr 3757  df-uni 3951  df-iota 5351  df-fv 5395  df-ov 6016
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