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Theorem dp2eq1 31785
Description: Equality theorem for the decimal expansion constructor. (Contributed by David A. Wheeler, 15-May-2015.)
Assertion
Ref Expression
dp2eq1 (𝐴 = 𝐵𝐴𝐶 = 𝐵𝐶)

Proof of Theorem dp2eq1
StepHypRef Expression
1 oveq1 7368 . 2 (𝐴 = 𝐵 → (𝐴 + (𝐶 / 10)) = (𝐵 + (𝐶 / 10)))
2 df-dp2 31784 . 2 𝐴𝐶 = (𝐴 + (𝐶 / 10))
3 df-dp2 31784 . 2 𝐵𝐶 = (𝐵 + (𝐶 / 10))
41, 2, 33eqtr4g 2798 1 (𝐴 = 𝐵𝐴𝐶 = 𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  (class class class)co 7361  0cc0 11059  1c1 11060   + caddc 11062   / cdiv 11820  cdc 12626  cdp2 31783
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 2704
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 2711  df-cleq 2725  df-clel 2811  df-rab 3407  df-v 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4287  df-if 4491  df-sn 4591  df-pr 4593  df-op 4597  df-uni 4870  df-br 5110  df-iota 6452  df-fv 6508  df-ov 7364  df-dp2 31784
This theorem is referenced by:  dp2eq1i  31787
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