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Theorem decex 10376
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 10375 . 2  |- ; A B  =  ( ( 10  x.  A
)  +  B )
2 ovex 6098 . 2  |-  ( ( 10  x.  A )  +  B )  e. 
_V
31, 2eqeltri 2505 1  |- ; A B  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1725   _Vcvv 2948  (class class class)co 6073    + caddc 8985    x. cmul 8987   10c10 10049  ;cdc 10374
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-nul 4330
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-sn 3812  df-pr 3813  df-uni 4008  df-iota 5410  df-fv 5454  df-ov 6076  df-dec 10375
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