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Theorem decex 10318
Description: A decimal number is a set. (Contributed by Mario Carneiro, 17-Apr-2015.)
Assertion
Ref Expression
decex  |- ; A B  e.  _V

Proof of Theorem decex
StepHypRef Expression
1 df-dec 10317 . 2  |- ; A B  =  ( ( 10  x.  A
)  +  B )
2 ovex 6047 . 2  |-  ( ( 10  x.  A )  +  B )  e. 
_V
31, 2eqeltri 2459 1  |- ; A B  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1717   _Vcvv 2901  (class class class)co 6022    + caddc 8928    x. cmul 8930   10c10 9991  ;cdc 10316
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370  ax-nul 4281
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2244  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-ne 2554  df-ral 2656  df-rex 2657  df-v 2903  df-sbc 3107  df-dif 3268  df-un 3270  df-in 3272  df-ss 3279  df-nul 3574  df-sn 3765  df-pr 3766  df-uni 3960  df-iota 5360  df-fv 5404  df-ov 6025  df-dec 10317
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