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Theorem deceq2 10318
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 6028 . 2  |-  ( A  =  B  ->  (
( 10  x.  C
)  +  A )  =  ( ( 10  x.  C )  +  B ) )
2 df-dec 10315 . 2  |- ; C A  =  ( ( 10  x.  C
)  +  A )
3 df-dec 10315 . 2  |- ; C B  =  ( ( 10  x.  C
)  +  B )
41, 2, 33eqtr4g 2444 1  |-  ( A  =  B  -> ; C A  = ; C B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649  (class class class)co 6020    + caddc 8926    x. cmul 8928   10c10 9989  ;cdc 10314
This theorem is referenced by:  deceq2i  10320
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 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-rex 2655  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-uni 3958  df-br 4154  df-iota 5358  df-fv 5402  df-ov 6023  df-dec 10315
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