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Theorem mulex 12922
Description: The multiplication operation is a set. (Contributed by NM, 19-Oct-2004.) (Revised by Mario Carneiro, 17-Nov-2014.)
Assertion
Ref Expression
mulex · ∈ V

Proof of Theorem mulex
StepHypRef Expression
1 ax-mulf 11139 . 2 · :(ℂ × ℂ)⟶ℂ
2 cnex 11140 . . 3 ℂ ∈ V
32, 2xpex 7691 . 2 (ℂ × ℂ) ∈ V
4 fex2 7874 . 2 (( · :(ℂ × ℂ)⟶ℂ ∧ (ℂ × ℂ) ∈ V ∧ ℂ ∈ V) → · ∈ V)
51, 3, 2, 4mp3an 1462 1 · ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3447   × cxp 5635  wf 6496  cc 11057   · cmul 11064
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5260  ax-nul 5267  ax-pow 5324  ax-pr 5388  ax-un 7676  ax-cnex 11115  ax-mulf 11139
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3062  df-rex 3071  df-rab 3407  df-v 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4287  df-if 4491  df-pw 4566  df-sn 4591  df-pr 4593  df-op 4597  df-uni 4870  df-br 5110  df-opab 5172  df-xp 5643  df-rel 5644  df-cnv 5645  df-dm 5647  df-rn 5648  df-fun 6502  df-fn 6503  df-f 6504
This theorem is referenced by:  cnfldmul  20825  cnfldfun  20831  cnfldfunALT  20832  cnfldfunALTOLD  20833  cnlmod4  24525  cnnvg  29669  cnnvs  29671  cncph  29810
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