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Theorem dfdec10 8561
Description: Version of the definition of the "decimal constructor" using ; 1 0 instead of the symbol 10. Of course, this statement cannot be used as definition, because it uses the "decimal constructor". (Contributed by AV, 1-Aug-2021.)
Assertion
Ref Expression
dfdec10  |- ; A B  =  ( (; 1 0  x.  A
)  +  B )

Proof of Theorem dfdec10
StepHypRef Expression
1 df-dec 8559 . 2  |- ; A B  =  ( ( ( 9  +  1 )  x.  A
)  +  B )
2 9p1e10 8560 . . . 4  |-  ( 9  +  1 )  = ; 1
0
32oveq1i 5553 . . 3  |-  ( ( 9  +  1 )  x.  A )  =  (; 1 0  x.  A
)
43oveq1i 5553 . 2  |-  ( ( ( 9  +  1 )  x.  A )  +  B )  =  ( (; 1 0  x.  A
)  +  B )
51, 4eqtri 2102 1  |- ; A B  =  ( (; 1 0  x.  A
)  +  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1285  (class class class)co 5543   0cc0 7043   1c1 7044    + caddc 7046    x. cmul 7048   9c9 8163  ;cdc 8558
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-cnex 7129  ax-resscn 7130  ax-1cn 7131  ax-1re 7132  ax-icn 7133  ax-addcl 7134  ax-addrcl 7135  ax-mulcl 7136  ax-mulcom 7139  ax-addass 7140  ax-mulass 7141  ax-distr 7142  ax-1rid 7145  ax-0id 7146  ax-cnre 7149
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-rab 2358  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-sn 3412  df-pr 3413  df-op 3415  df-uni 3610  df-int 3645  df-br 3794  df-iota 4897  df-fv 4940  df-ov 5546  df-inn 8107  df-2 8165  df-3 8166  df-4 8167  df-5 8168  df-6 8169  df-7 8170  df-8 8171  df-9 8172  df-dec 8559
This theorem is referenced by:  decnncl  8577  dec0u  8578  dec0h  8579  decnncl2  8581  declt  8585  decltc  8586  decsuc  8588  decle  8591  declti  8595  decsucc  8598  dec10p  8600  decma  8608  decmac  8609  decma2c  8610  decadd  8611  decaddc  8612  decsubi  8620  decmul1  8621  decmul1c  8622  decmul2c  8623  decmul10add  8626  5t5e25  8660  6t6e36  8665  8t6e48  8676  9t11e99  8687  3dec  9739  3dvdsdec  10409
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