Theorem deceq12i 9190

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

Hypotheses

Ref	Expression
deceq1i.1	|- A = B
deceq12i.2	|- C = D

Assertion

Ref	Expression
deceq12i	|- ; A C = ; B D

Proof of Theorem deceq12i

Step	Hyp	Ref	Expression
1		deceq1i.1	. . 3 |- A = B
2	1	deceq1i 9188	. 2 |- ; A C = ; B C
3		deceq12i.2	. . 3 |- C = D
4	3	deceq2i 9189	. 2 |- ; B C = ; B D
5	2, 4	eqtri 2160	1 |- ; A C = ; B D

Syntax hints:   = wceq 1331  ;cdc 9182

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-iota 5088  df-fv 5131  df-ov 5777  df-dec 9183

This theorem is referenced by:  11multnc  9249