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Theorem addex 11868
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 10053 . 2 + :(ℂ × ℂ)⟶ℂ
2 cnex 10055 . . 3 ℂ ∈ V
32, 2xpex 7004 . 2 (ℂ × ℂ) ∈ V
4 fex2 7163 . 2 (( + :(ℂ × ℂ)⟶ℂ ∧ (ℂ × ℂ) ∈ V ∧ ℂ ∈ V) → + ∈ V)
51, 3, 2, 4mp3an 1464 1 + ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2030  Vcvv 3231   × cxp 5141  wf 5922  cc 9972   + caddc 9977
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-8 2032  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814  ax-nul 4822  ax-pow 4873  ax-pr 4936  ax-un 6991  ax-cnex 10030  ax-addf 10053
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-eu 2502  df-mo 2503  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946  df-rex 2947  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-pw 4193  df-sn 4211  df-pr 4213  df-op 4217  df-uni 4469  df-br 4686  df-opab 4746  df-xp 5149  df-rel 5150  df-cnv 5151  df-dm 5153  df-rn 5154  df-fun 5928  df-fn 5929  df-f 5930
This theorem is referenced by:  cnaddablx  18317  cnaddabl  18318  cnaddid  18319  cnaddinv  18320  zaddablx  18321  cnfldadd  19799  cnfldfun  19806  cnfldfunALT  19807  cnlmodlem2  22983  cnnvg  27661  cnnvs  27663  cncph  27802  cnaddcom  34577
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