Theorem deceq12i 9330

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 9328	. 2 |- ; A C = ; B C
3		deceq12i.2	. . 3 |- C = D
4	3	deceq2i 9329	. 2 |- ; B C = ; B D
5	2, 4	eqtri 2186	1 |- ; A C = ; B D

Syntax hints:   = wceq 1343  ;cdc 9322

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 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-3an 970  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-rex 2450  df-v 2728  df-un 3120  df-sn 3582  df-pr 3583  df-op 3585  df-uni 3790  df-br 3983  df-iota 5153  df-fv 5196  df-ov 5845  df-dec 9323

This theorem is referenced by:  11multnc  9389