Theorem deceq1i 9366

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 9364	. 2 |- ( A = B -> ; A C = ; B C )
3	1, 2	ax-mp 5	1 |- ; A C = ; B C

Syntax hints:   = wceq 1353  ;cdc 9360

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2739  df-un 3133  df-sn 3597  df-pr 3598  df-op 3600  df-uni 3808  df-br 4001  df-iota 5173  df-fv 5219  df-ov 5871  df-dec 9361

This theorem is referenced by:  deceq12i  9368  decmul10add  9428