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Theorem deceq1i 12738
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 12736 . 2 (𝐴 = 𝐵𝐴𝐶 = 𝐵𝐶)
31, 2ax-mp 5 1 𝐴𝐶 = 𝐵𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  cdc 12731
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-iota 6516  df-fv 6571  df-ov 7434  df-dec 12732
This theorem is referenced by:  deceq12i  12740  decmul10add  12800  1mhdrd  32883  hgt750lem2  34646  sqn5ii  42300  fmtno5lem4  47481  fmtno5fac  47507
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