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Theorem addex 12032
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 10216 . 2 + :(ℂ × ℂ)⟶ℂ
2 cnex 10218 . . 3 ℂ ∈ V
32, 2xpex 7108 . 2 (ℂ × ℂ) ∈ V
4 fex2 7267 . 2 (( + :(ℂ × ℂ)⟶ℂ ∧ (ℂ × ℂ) ∈ V ∧ ℂ ∈ V) → + ∈ V)
51, 3, 2, 4mp3an 1571 1 + ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2144  Vcvv 3349   × cxp 5247  wf 6027  cc 10135   + caddc 10140
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-8 2146  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750  ax-sep 4912  ax-nul 4920  ax-pow 4971  ax-pr 5034  ax-un 7095  ax-cnex 10193  ax-addf 10216
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-eu 2621  df-mo 2622  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-ral 3065  df-rex 3066  df-rab 3069  df-v 3351  df-dif 3724  df-un 3726  df-in 3728  df-ss 3735  df-nul 4062  df-if 4224  df-pw 4297  df-sn 4315  df-pr 4317  df-op 4321  df-uni 4573  df-br 4785  df-opab 4845  df-xp 5255  df-rel 5256  df-cnv 5257  df-dm 5259  df-rn 5260  df-fun 6033  df-fn 6034  df-f 6035
This theorem is referenced by:  cnaddablx  18477  cnaddabl  18478  cnaddid  18479  cnaddinv  18480  zaddablx  18481  cnfldadd  19965  cnfldfun  19972  cnfldfunALT  19973  cnlmodlem2  23155  cnnvg  27867  cnnvs  27869  cncph  28008  cnaddcom  34774
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