Theorem decex 12615

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 12612	. 2 ⊢ ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
2	1	ovexi 7394	1 ⊢ ;𝐴𝐵 ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3441  (class class class)co 7360  1c1 11031   + caddc 11033   · cmul 11035  9c9 12211  ;cdc 12611

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-nul 5252

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ne 2934  df-v 3443  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4287  df-sn 4582  df-pr 4584  df-uni 4865  df-iota 6449  df-fv 6501  df-ov 7363  df-dec 12612

This theorem is referenced by:  nfermltl2rev  48031