Theorem deceq2i 12657

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 12655	. 2 ⊢ (𝐴 = 𝐵 → ;𝐶𝐴 = ;𝐶𝐵)
3	1, 2	ax-mp 5	1 ⊢ ;𝐶𝐴 = ;𝐶𝐵

Syntax hints:   = wceq 1541  ;cdc 12649

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3426  df-v 3468  df-dif 3938  df-un 3940  df-in 3942  df-ss 3952  df-nul 4310  df-if 4514  df-sn 4614  df-pr 4616  df-op 4620  df-uni 4893  df-br 5133  df-iota 6475  df-fv 6531  df-ov 7387  df-dec 12650

This theorem is referenced by:  deceq12i  12658  sqn5i  40897