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Theorem decex 12678
Description: A decimal number is a set. (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 6-Sep-2021.)
Assertion
Ref Expression
decex 𝐴𝐵 ∈ V

Proof of Theorem decex
StepHypRef Expression
1 df-dec 12675 . 2 𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
21ovexi 7440 1 𝐴𝐵 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3475  (class class class)co 7406  1c1 11108   + caddc 11110   · cmul 11112  9c9 12271  cdc 12674
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-nul 5306
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ne 2942  df-v 3477  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-sn 4629  df-pr 4631  df-uni 4909  df-iota 6493  df-fv 6549  df-ov 7409  df-dec 12675
This theorem is referenced by:  nfermltl2rev  46398
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