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Theorem deceq1i 12626
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 12624 . 2 (𝐴 = 𝐵𝐴𝐶 = 𝐵𝐶)
31, 2ax-mp 5 1 𝐴𝐶 = 𝐵𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cdc 12619
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3409  df-v 3448  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-uni 4867  df-br 5107  df-iota 6449  df-fv 6505  df-ov 7361  df-dec 12620
This theorem is referenced by:  deceq12i  12628  decmul10add  12688  1mhdrd  31775  hgt750lem2  33268  sqn5ii  40803  fmtno5lem4  45755  fmtno5fac  45781
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