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Theorem deceq2 9155
Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 6-Sep-2021.)
Assertion
Ref Expression
deceq2  |-  ( A  =  B  -> ; C A  = ; C B )

Proof of Theorem deceq2
StepHypRef Expression
1 oveq2 5750 . 2  |-  ( A  =  B  ->  (
( ( 9  +  1 )  x.  C
)  +  A )  =  ( ( ( 9  +  1 )  x.  C )  +  B ) )
2 df-dec 9151 . 2  |- ; C A  =  ( ( ( 9  +  1 )  x.  C
)  +  A )
3 df-dec 9151 . 2  |- ; C B  =  ( ( ( 9  +  1 )  x.  C
)  +  B )
41, 2, 33eqtr4g 2175 1  |-  ( A  =  B  -> ; C A  = ; C B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1316  (class class class)co 5742   1c1 7589    + caddc 7591    x. cmul 7593   9c9 8746  ;cdc 9150
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-un 3045  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-iota 5058  df-fv 5101  df-ov 5745  df-dec 9151
This theorem is referenced by:  deceq2i  9157
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