Theorem decex 12719

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 12716	. 2 ⊢ ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
2	1	ovexi 7444	1 ⊢ ;𝐴𝐵 ∈ V

This proof depends on syntax axioms:   ∈ wcel 2143  Vcvv 3455  (class class class)co 7410  1c1 11105   + caddc 11107   · cmul 11109  9c9 12306  ;cdc 12715

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-nul 5269

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-ne 2959  df-v 3457  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-sn 4590  df-pr 4592  df-uni 4873  df-iota 6492  df-fv 6544  df-ov 7413  df-dec 12716

This theorem is used by:  nfermltl2rev  48536