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Theorem addex 11103
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 9475 . 2  |-  +  :
( CC  X.  CC )
--> CC
2 cnex 9477 . . 3  |-  CC  e.  _V
32, 2xpex 6621 . 2  |-  ( CC 
X.  CC )  e. 
_V
4 fex2 6645 . 2  |-  ( (  +  : ( CC 
X.  CC ) --> CC 
/\  ( CC  X.  CC )  e.  _V  /\  CC  e.  _V )  ->  +  e.  _V )
51, 3, 2, 4mp3an 1315 1  |-  +  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1758   _Vcvv 3078    X. cxp 4949   -->wf 5525   CCcc 9394    + caddc 9399
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4524  ax-nul 4532  ax-pow 4581  ax-pr 4642  ax-un 6485  ax-cnex 9452  ax-addf 9475
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-if 3903  df-pw 3973  df-sn 3989  df-pr 3991  df-op 3995  df-uni 4203  df-br 4404  df-opab 4462  df-xp 4957  df-rel 4958  df-cnv 4959  df-dm 4961  df-rn 4962  df-fun 5531  df-fn 5532  df-f 5533
This theorem is referenced by:  cnaddablx  16472  cnaddabl  16473  zaddablx  16474  cnfldadd  17951  cnnvg  24240  cnnvs  24243  cncph  24391  cnaddcom  32975
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