Theorem deceq1i 8483

Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.)

Hypothesis

Ref	Expression
deceq1i.1	|- A = B

Assertion

Ref	Expression
deceq1i	|- ; A C = ; B C

Proof of Theorem deceq1i

Step	Hyp	Ref	Expression
1		deceq1i.1	. 2 |- A = B
2		deceq1 8481	. 2 |- ( A = B -> ; A C = ; B C )
3	1, 2	ax-mp 7	1 |- ; A C = ; B C

Syntax hints:   = wceq 1284  ;cdc 8477

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 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-3an 921  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-rex 2354  df-v 2603  df-un 2977  df-sn 3404  df-pr 3405  df-op 3407  df-uni 3602  df-br 3786  df-iota 4887  df-fv 4930  df-ov 5535  df-dec 8478

This theorem is referenced by:  deceq12i  8485  decmul10add  8545