Theorem decex 12126

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 12123	. 2 ⊢ ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
2	1	ovexi 7177	1 ⊢ ;𝐴𝐵 ∈ V

Syntax hints:   ∈ wcel 2112  Vcvv 3407  (class class class)co 7143  1c1 10561   + caddc 10563   · cmul 10565  9c9 11721  ;cdc 12122

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2730  ax-nul 5169

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 846  df-tru 1542  df-ex 1783  df-nf 1787  df-sb 2071  df-mo 2558  df-eu 2589  df-clab 2737  df-cleq 2751  df-clel 2831  df-ral 3073  df-rex 3074  df-v 3409  df-sbc 3694  df-dif 3857  df-un 3859  df-in 3861  df-ss 3871  df-nul 4222  df-sn 4516  df-pr 4518  df-uni 4792  df-iota 6287  df-fv 6336  df-ov 7146  df-dec 12123

This theorem is referenced by:  nfermltl2rev  44613