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Theorem addex 10981
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 9353 . 2  |-  +  :
( CC  X.  CC )
--> CC
2 cnex 9355 . . 3  |-  CC  e.  _V
32, 2xpex 6503 . 2  |-  ( CC 
X.  CC )  e. 
_V
4 fex2 6527 . 2  |-  ( (  +  : ( CC 
X.  CC ) --> CC 
/\  ( CC  X.  CC )  e.  _V  /\  CC  e.  _V )  ->  +  e.  _V )
51, 3, 2, 4mp3an 1314 1  |-  +  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1756   _Vcvv 2967    X. cxp 4833   -->wf 5409   CCcc 9272    + caddc 9277
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-8 1758  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419  ax-sep 4408  ax-nul 4416  ax-pow 4465  ax-pr 4526  ax-un 6367  ax-cnex 9330  ax-addf 9353
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2256  df-mo 2257  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2715  df-rex 2716  df-rab 2719  df-v 2969  df-dif 3326  df-un 3328  df-in 3330  df-ss 3337  df-nul 3633  df-if 3787  df-pw 3857  df-sn 3873  df-pr 3875  df-op 3879  df-uni 4087  df-br 4288  df-opab 4346  df-xp 4841  df-rel 4842  df-cnv 4843  df-dm 4845  df-rn 4846  df-fun 5415  df-fn 5416  df-f 5417
This theorem is referenced by:  cnaddablx  16339  cnaddabl  16340  zaddablx  16341  cnfldadd  17798  cnnvg  24019  cnnvs  24022  cncph  24170  cnaddcom  32457
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