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Theorem deceq2 10378
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 6081 . 2  |-  ( A  =  B  ->  (
( 10  x.  C
)  +  A )  =  ( ( 10  x.  C )  +  B ) )
2 df-dec 10375 . 2  |- ; C A  =  ( ( 10  x.  C
)  +  A )
3 df-dec 10375 . 2  |- ; C B  =  ( ( 10  x.  C
)  +  B )
41, 2, 33eqtr4g 2492 1  |-  ( A  =  B  -> ; C A  = ; C B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652  (class class class)co 6073    + caddc 8985    x. cmul 8987   10c10 10049  ;cdc 10374
This theorem is referenced by:  deceq2i  10380
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
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076  df-dec 10375
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