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Theorem deceq1i 9195
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 9193 . 2 (𝐴 = 𝐵𝐴𝐶 = 𝐵𝐶)
31, 2ax-mp 5 1 𝐴𝐶 = 𝐵𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1331  cdc 9189
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-iota 5088  df-fv 5131  df-ov 5777  df-dec 9190
This theorem is referenced by:  deceq12i  9197  decmul10add  9257
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