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Theorem addex 12365
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 10593 . 2 + :(ℂ × ℂ)⟶ℂ
2 cnex 10595 . . 3 ℂ ∈ V
32, 2xpex 7451 . 2 (ℂ × ℂ) ∈ V
4 fex2 7613 . 2 (( + :(ℂ × ℂ)⟶ℂ ∧ (ℂ × ℂ) ∈ V ∧ ℂ ∈ V) → + ∈ V)
51, 3, 2, 4mp3an 1458 1 + ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2115  Vcvv 3471   × cxp 5526  wf 6324  cc 10512   + caddc 10517
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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2178  ax-ext 2793  ax-sep 5176  ax-nul 5183  ax-pow 5239  ax-pr 5303  ax-un 7436  ax-cnex 10570  ax-addf 10593
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2623  df-eu 2654  df-clab 2800  df-cleq 2814  df-clel 2892  df-nfc 2960  df-ral 3131  df-rex 3132  df-rab 3135  df-v 3473  df-dif 3913  df-un 3915  df-in 3917  df-ss 3927  df-nul 4267  df-if 4441  df-pw 4514  df-sn 4541  df-pr 4543  df-op 4547  df-uni 4812  df-br 5040  df-opab 5102  df-xp 5534  df-rel 5535  df-cnv 5536  df-dm 5538  df-rn 5539  df-fun 6330  df-fn 6331  df-f 6332
This theorem is referenced by:  cnaddablx  18967  cnaddabl  18968  cnaddid  18969  cnaddinv  18970  zaddablx  18971  cnfldadd  20526  cnfldfun  20533  cnfldfunALT  20534  cnlmodlem2  23721  cnnvg  28440  cnnvs  28442  cncph  28581  cnaddcom  36154  nn0mnd  44262
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