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Theorem deceq2i 8373
 Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.)
Hypothesis
Ref Expression
deceq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
deceq2i 𝐶𝐴 = 𝐶𝐵

Proof of Theorem deceq2i
StepHypRef Expression
1 deceq1i.1 . 2 𝐴 = 𝐵
2 deceq2 8371 . 2 (𝐴 = 𝐵𝐶𝐴 = 𝐶𝐵)
31, 2ax-mp 7 1 𝐶𝐴 = 𝐶𝐵
 Colors of variables: wff set class Syntax hints:   = wceq 1243  ;cdc 8368 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515  df-dec 8369 This theorem is referenced by:  deceq12i  8374
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