Theorem decex 12721

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 12718	. 2 ⊢ ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
2	1	ovexi 7448	1 ⊢ ;𝐴𝐵 ∈ V

Syntax hints:   ∈ wcel 2107  Vcvv 3464  (class class class)co 7414  1c1 11139   + caddc 11141   · cmul 11143  9c9 12311  ;cdc 12717

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706  ax-nul 5288

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-ne 2932  df-v 3466  df-dif 3936  df-un 3938  df-ss 3950  df-nul 4316  df-sn 4609  df-pr 4611  df-uni 4890  df-iota 6495  df-fv 6550  df-ov 7417  df-dec 12718

This theorem is referenced by:  nfermltl2rev  47676