Theorem deceq12i 9680

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 9678	. 2 |- ; A C = ; B C
3		deceq12i.2	. . 3 |- C = D
4	3	deceq2i 9679	. 2 |- ; B C = ; B D
5	2, 4	eqtri 2252	1 |- ; A C = ; B D

Syntax hints:   = wceq 1398  ;cdc 9672

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-rex 2517  df-v 2805  df-un 3205  df-sn 3679  df-pr 3680  df-op 3682  df-uni 3899  df-br 4094  df-iota 5293  df-fv 5341  df-ov 6031  df-dec 9673

This theorem is referenced by:  11multnc  9739