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Theorem ballotlemoex 24743
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 6106 . . 3  |-  ( 1 ... ( M  +  N ) )  e. 
_V
21pwex 4382 . 2  |-  ~P (
1 ... ( M  +  N ) )  e. 
_V
3 ballotth.o . . 3  |-  O  =  { c  e.  ~P ( 1 ... ( M  +  N )
)  |  ( # `  c )  =  M }
4 ssrab2 3428 . . 3  |-  { c  e.  ~P ( 1 ... ( M  +  N ) )  |  ( # `  c
)  =  M }  C_ 
~P ( 1 ... ( M  +  N
) )
53, 4eqsstri 3378 . 2  |-  O  C_  ~P ( 1 ... ( M  +  N )
)
62, 5ssexi 4348 1  |-  O  e. 
_V
Colors of variables: wff set class
Syntax hints:    = wceq 1652    e. wcel 1725   {crab 2709   _Vcvv 2956   ~Pcpw 3799   ` cfv 5454  (class class class)co 6081   1c1 8991    + caddc 8993   NNcn 10000   ...cfz 11043   #chash 11618
This theorem is referenced by:  ballotlem2  24746  ballotlem8  24794
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-pw 3801  df-sn 3820  df-pr 3821  df-uni 4016  df-iota 5418  df-fv 5462  df-ov 6084
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