Theorem deceq2i 9325

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	⊢ ;𝐶𝐴 = ;𝐶𝐵

Proof of Theorem deceq2i

Step	Hyp	Ref	Expression
1		deceq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		deceq2 9323	. 2 ⊢ (𝐴 = 𝐵 → ;𝐶𝐴 = ;𝐶𝐵)
3	1, 2	ax-mp 5	1 ⊢ ;𝐶𝐴 = ;𝐶𝐵

Syntax hints:   = wceq 1343  ;cdc 9318

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 2296  df-rex 2449  df-v 2727  df-un 3119  df-sn 3581  df-pr 3582  df-op 3584  df-uni 3789  df-br 3982  df-iota 5152  df-fv 5195  df-ov 5844  df-dec 9319

This theorem is referenced by:  deceq12i  9326