Theorem deceq2i 9182

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

Hypothesis

Ref	Expression
deceq1i.1	|- A = B

Assertion

Ref	Expression
deceq2i	|- ; C A = ; C B

Proof of Theorem deceq2i

Step	Hyp	Ref	Expression
1		deceq1i.1	. 2 |- A = B
2		deceq2 9180	. 2 |- ( A = B -> ; C A = ; C B )
3	1, 2	ax-mp 5	1 |- ; C A = ; C B

Syntax hints:   = wceq 1331  ;cdc 9175

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 2119

This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-uni 3732  df-br 3925  df-iota 5083  df-fv 5126  df-ov 5770  df-dec 9176

This theorem is referenced by:  deceq12i  9183