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Theorem dp2eq2i 32832
Description: Equality theorem for the decimal expansion constructor. (Contributed by David A. Wheeler, 15-May-2015.)
Hypothesis
Ref Expression
dp2eq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
dp2eq2i 𝐶𝐴 = 𝐶𝐵

Proof of Theorem dp2eq2i
StepHypRef Expression
1 dp2eq1i.1 . 2 𝐴 = 𝐵
2 dp2eq2 32830 . 2 (𝐴 = 𝐵𝐶𝐴 = 𝐶𝐵)
31, 2ax-mp 5 1 𝐶𝐴 = 𝐶𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  cdp2 32827
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2105  ax-9 2113  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2712  df-cleq 2726  df-clel 2813  df-rab 3439  df-v 3484  df-dif 3973  df-un 3975  df-ss 3987  df-nul 4348  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-uni 4932  df-br 5170  df-iota 6524  df-fv 6580  df-ov 7448  df-dp2 32828
This theorem is referenced by:  dp2eq12i  32833  hgt750lem2  34621
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