Theorem decex 12609

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

Step	Hyp	Ref	Expression
1		df-dec 12606	. 2 ⊢ ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
2	1	ovexi 7390	1 ⊢ ;𝐴𝐵 ∈ V

Syntax hints:   ∈ wcel 2113  Vcvv 3438  (class class class)co 7356  1c1 11025   + caddc 11027   · cmul 11029  9c9 12205  ;cdc 12605

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2706  ax-nul 5249

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-ne 2931  df-v 3440  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4284  df-sn 4579  df-pr 4581  df-uni 4862  df-iota 6446  df-fv 6498  df-ov 7359  df-dec 12606

This theorem is referenced by:  nfermltl2rev  47931