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Theorem deceq2 10130
Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.)
Assertion
Ref Expression
deceq2  |-  ( A  =  B  -> ; C A  = ; C B )

Proof of Theorem deceq2
StepHypRef Expression
1 oveq2 5868 . 2  |-  ( A  =  B  ->  (
( 10  x.  C
)  +  A )  =  ( ( 10  x.  C )  +  B ) )
2 df-dec 10127 . 2  |- ; C A  =  ( ( 10  x.  C
)  +  A )
3 df-dec 10127 . 2  |- ; C B  =  ( ( 10  x.  C
)  +  B )
41, 2, 33eqtr4g 2342 1  |-  ( A  =  B  -> ; C A  = ; C B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1625  (class class class)co 5860    + caddc 8742    x. cmul 8744   10c10 9805  ;cdc 10126
This theorem is referenced by:  deceq2i  10132
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-rex 2551  df-rab 2554  df-v 2792  df-dif 3157  df-un 3159  df-in 3161  df-ss 3168  df-nul 3458  df-if 3568  df-sn 3648  df-pr 3649  df-op 3651  df-uni 3830  df-br 4026  df-iota 5221  df-fv 5265  df-ov 5863  df-dec 10127
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