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Theorem deceq1i 12740
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 𝐴𝐶 = 𝐵𝐶

Proof of Theorem deceq1i
StepHypRef Expression
1 deceq1i.1 . 2 𝐴 = 𝐵
2 deceq1 12738 . 2 (𝐴 = 𝐵𝐴𝐶 = 𝐵𝐶)
31, 2ax-mp 5 1 𝐴𝐶 = 𝐵𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  cdc 12733
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-iota 6514  df-fv 6569  df-ov 7434  df-dec 12734
This theorem is referenced by:  deceq12i  12742  decmul10add  12802  1mhdrd  32898  hgt750lem2  34667  sqn5ii  42321  fmtno5lem4  47543  fmtno5fac  47569
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