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Theorem addex 13031
Description: The addition operation is a set. (Contributed by NM, 19-Oct-2004.) (Revised by Mario Carneiro, 17-Nov-2014.)
Assertion
Ref Expression
addex + ∈ V

Proof of Theorem addex
StepHypRef Expression
1 ax-addf 11234 . 2 + :(ℂ × ℂ)⟶ℂ
2 cnex 11236 . . 3 ℂ ∈ V
32, 2xpex 7773 . 2 (ℂ × ℂ) ∈ V
4 fex2 7958 . 2 (( + :(ℂ × ℂ)⟶ℂ ∧ (ℂ × ℂ) ∈ V ∧ ℂ ∈ V) → + ∈ V)
51, 3, 2, 4mp3an 1463 1 + ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  Vcvv 3480   × cxp 5683  wf 6557  cc 11153   + caddc 11158
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pow 5365  ax-pr 5432  ax-un 7755  ax-cnex 11211  ax-addf 11234
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-nul 4334  df-if 4526  df-pw 4602  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-opab 5206  df-xp 5691  df-rel 5692  df-cnv 5693  df-dm 5695  df-rn 5696  df-fun 6563  df-fn 6564  df-f 6565
This theorem is referenced by:  cnaddablx  19886  cnaddabl  19887  cnaddid  19888  cnaddinv  19889  zaddablx  19890  cnfldaddOLD  21384  cnfldfunOLD  21391  cnfldfunALTOLD  21392  cnfldfunALTOLDOLD  21393  cnlmodlem2  25170  cnnvg  30697  cnnvs  30699  cncph  30838  cnaddcom  38973  nn0mnd  48095
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