Theorem decex 11498

Description: A decimal number is a set. (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 6-Sep-2021.)

Assertion

Ref	Expression
decex	|- ; A B e. _V

Proof of Theorem decex

Step	Hyp	Ref	Expression
1		df-dec 11494	. 2 |- ; A B = ( ( ( 9 + 1 ) x. A ) + B )
2	1	ovexi 6679	1 |- ; A B e. _V

Syntax hints:   e. wcel 1990   _Vcvv 3200  (class class class)co 6650   1c1 9937   + caddc 9939   x. cmul 9941   9c9 11077  ;cdc 11493

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-nul 4789

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-eu 2474  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rex 2918  df-v 3202  df-sbc 3436  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-sn 4178  df-pr 4180  df-uni 4437  df-iota 5851  df-fv 5896  df-ov 6653  df-dec 11494

This theorem is referenced by: (None)