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Theorem addex 10602
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 9061 . 2  |-  +  :
( CC  X.  CC )
--> CC
2 cnex 9063 . . 3  |-  CC  e.  _V
32, 2xpex 4982 . 2  |-  ( CC 
X.  CC )  e. 
_V
4 fex2 5595 . 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 1725   _Vcvv 2948    X. cxp 4868   -->wf 5442   CCcc 8980    + caddc 8985
This theorem is referenced by:  cnaddablx  15473  cnaddabl  15474  zaddablx  15475  cnfldadd  16700  cnnvg  22161  cnnvs  22164  cncph  22312  cnaddcom  29696
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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395  ax-un 4693  ax-cnex 9038  ax-addf 9061
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-xp 4876  df-rel 4877  df-cnv 4878  df-dm 4880  df-rn 4881  df-fun 5448  df-fn 5449  df-f 5450
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