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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
StepHypRef Expression
1 deceq1i.1 . 2 𝐴 = 𝐵
2 deceq2 12655 . 2 (𝐴 = 𝐵𝐶𝐴 = 𝐶𝐵)
31, 2ax-mp 5 1 𝐶𝐴 = 𝐶𝐵
Colors of variables: wff setvar class
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
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