Theorem decex 12831

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 12828	. 2 ⊢ ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
2	1	ovexi 7464	1 ⊢ ;𝐴𝐵 ∈ V

This proof depends on syntax axioms:   ∈ wcel 2146  Vcvv 3454  (class class class)co 7430  1c1 11214   + caddc 11216   · cmul 11218  9c9 12417  ;cdc 12827

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735  ax-nul 5263

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2839  df-ne 2960  df-v 3456  df-ss 3901  df-dif 4050  df-un 4154  df-nul 4282  df-sn 4589  df-pr 4591  df-uni 4871  df-iota 6501  df-fv 6555  df-ov 7433  df-dec 12828

This theorem is used by:  nfermltl2rev  48986