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Theorem deceq2 10144
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 5882 . 2  |-  ( A  =  B  ->  (
( 10  x.  C
)  +  A )  =  ( ( 10  x.  C )  +  B ) )
2 df-dec 10141 . 2  |- ; C A  =  ( ( 10  x.  C
)  +  A )
3 df-dec 10141 . 2  |- ; C B  =  ( ( 10  x.  C
)  +  B )
41, 2, 33eqtr4g 2353 1  |-  ( A  =  B  -> ; C A  = ; C B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632  (class class class)co 5874    + caddc 8756    x. cmul 8758   10c10 9819  ;cdc 10140
This theorem is referenced by:  deceq2i  10146
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877  df-dec 10141
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