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Theorem addex 10542
Description: The addition operation is a set. (Contributed by NM, 19-Oct-2004.) (Revised by Mario Carneiro, 17-Nov-2014.)
Assertion
Ref Expression
addex  |-  +  e.  _V

Proof of Theorem addex
StepHypRef Expression
1 ax-addf 9002 . 2  |-  +  :
( CC  X.  CC )
--> CC
2 cnex 9004 . . 3  |-  CC  e.  _V
32, 2xpex 4930 . 2  |-  ( CC 
X.  CC )  e. 
_V
4 fex2 5543 . 2  |-  ( (  +  : ( CC 
X.  CC ) --> CC 
/\  ( CC  X.  CC )  e.  _V  /\  CC  e.  _V )  ->  +  e.  _V )
51, 3, 2, 4mp3an 1279 1  |-  +  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1717   _Vcvv 2899    X. cxp 4816   -->wf 5390   CCcc 8921    + caddc 8926
This theorem is referenced by:  cnaddablx  15408  cnaddabl  15409  zaddablx  15410  cnfldadd  16631  cnnvg  22017  cnnvs  22020  cncph  22168  cnaddcom  29086
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-13 1719  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-sep 4271  ax-nul 4279  ax-pow 4318  ax-pr 4344  ax-un 4641  ax-cnex 8979  ax-addf 9002
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2242  df-mo 2243  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-ral 2654  df-rex 2655  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-pw 3744  df-sn 3763  df-pr 3764  df-op 3766  df-uni 3958  df-br 4154  df-opab 4208  df-xp 4824  df-rel 4825  df-cnv 4826  df-dm 4828  df-rn 4829  df-fun 5396  df-fn 5397  df-f 5398
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