Theorem decex 12669

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 12666	. 2 ⊢ ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
2	1	ovexi 7428	1 ⊢ ;𝐴𝐵 ∈ V

Syntax hints:   ∈ wcel 2109  Vcvv 3455  (class class class)co 7394  1c1 11087   + caddc 11089   · cmul 11091  9c9 12259  ;cdc 12665

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702  ax-nul 5269

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-ne 2928  df-v 3457  df-dif 3925  df-un 3927  df-ss 3939  df-nul 4305  df-sn 4598  df-pr 4600  df-uni 4880  df-iota 6472  df-fv 6527  df-ov 7397  df-dec 12666

This theorem is referenced by:  nfermltl2rev  47699