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Theorem addex 12912
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 11129 . 2 + :(ℂ × ℂ)⟶ℂ
2 cnex 11131 . . 3 ℂ ∈ V
32, 2xpex 7686 . 2 (ℂ × ℂ) ∈ V
4 fex2 7869 . 2 (( + :(ℂ × ℂ)⟶ℂ ∧ (ℂ × ℂ) ∈ V ∧ ℂ ∈ V) → + ∈ V)
51, 3, 2, 4mp3an 1461 1 + ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2106  Vcvv 3445   × cxp 5631  wf 6492  cc 11048   + caddc 11053
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707  ax-sep 5256  ax-nul 5263  ax-pow 5320  ax-pr 5384  ax-un 7671  ax-cnex 11106  ax-addf 11129
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-ral 3065  df-rex 3074  df-rab 3408  df-v 3447  df-dif 3913  df-un 3915  df-in 3917  df-ss 3927  df-nul 4283  df-if 4487  df-pw 4562  df-sn 4587  df-pr 4589  df-op 4593  df-uni 4866  df-br 5106  df-opab 5168  df-xp 5639  df-rel 5640  df-cnv 5641  df-dm 5643  df-rn 5644  df-fun 6498  df-fn 6499  df-f 6500
This theorem is referenced by:  cnaddablx  19644  cnaddabl  19645  cnaddid  19646  cnaddinv  19647  zaddablx  19648  cnfldadd  20799  cnfldfun  20806  cnfldfunALT  20807  cnfldfunALTOLD  20808  cnlmodlem2  24498  cnnvg  29618  cnnvs  29620  cncph  29759  cnaddcom  37425  nn0mnd  46085
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