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Theorem ballotlemoex 23060
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 5899 . . 3  |-  ( 1 ... ( M  +  N ) )  e. 
_V
21pwex 4209 . 2  |-  ~P (
1 ... ( M  +  N ) )  e. 
_V
3 ballotth.o . . 3  |-  O  =  { c  e.  ~P ( 1 ... ( M  +  N )
)  |  ( # `  c )  =  M }
4 ssrab2 3271 . . 3  |-  { c  e.  ~P ( 1 ... ( M  +  N ) )  |  ( # `  c
)  =  M }  C_ 
~P ( 1 ... ( M  +  N
) )
53, 4eqsstri 3221 . 2  |-  O  C_  ~P ( 1 ... ( M  +  N )
)
62, 5ssexi 4175 1  |-  O  e. 
_V
Colors of variables: wff set class
Syntax hints:    = wceq 1632    e. wcel 1696   {crab 2560   _Vcvv 2801   ~Pcpw 3638   ` cfv 5271  (class class class)co 5874   1c1 8754    + caddc 8756   NNcn 9762   ...cfz 10798   #chash 11353
This theorem is referenced by:  ballotlem2  23063  ballotlem8  23111
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pow 4204
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-pw 3640  df-sn 3659  df-pr 3660  df-uni 3844  df-iota 5235  df-fv 5279  df-ov 5877
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