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Theorem deceq1i 12720
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 12718 . 2 (𝐴 = 𝐵𝐴𝐶 = 𝐵𝐶)
31, 2ax-mp 5 1 𝐴𝐶 = 𝐵𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  cdc 12713
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-rab 3429  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4325  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4911  df-br 5151  df-iota 6503  df-fv 6559  df-ov 7427  df-dec 12714
This theorem is referenced by:  deceq12i  12722  decmul10add  12782  1mhdrd  32657  hgt750lem2  34289  sqn5ii  41863  fmtno5lem4  46898  fmtno5fac  46924
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