Theorem decex 12694

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 12691	. 2 ⊢ ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
2	1	ovexi 7432	1 ⊢ ;𝐴𝐵 ∈ V

Syntax hints:   ∈ wcel 2144  Vcvv 3456  (class class class)co 7398  1c1 11076   + caddc 11078   · cmul 11080  9c9 12281  ;cdc 12690

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-ext 2736  ax-nul 5258

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1565  df-fal 1575  df-ex 1802  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-ne 2960  df-v 3458  df-dif 3909  df-un 3911  df-ss 3923  df-nul 4288  df-sn 4585  df-pr 4587  df-uni 4868  df-iota 6479  df-fv 6531  df-ov 7401  df-dec 12691

This theorem is referenced by:  nfermltl2rev  48370