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Theorem deceq12i 9309
Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.)
Hypotheses
Ref Expression
deceq1i.1 𝐴 = 𝐵
deceq12i.2 𝐶 = 𝐷
Assertion
Ref Expression
deceq12i 𝐴𝐶 = 𝐵𝐷

Proof of Theorem deceq12i
StepHypRef Expression
1 deceq1i.1 . . 3 𝐴 = 𝐵
21deceq1i 9307 . 2 𝐴𝐶 = 𝐵𝐶
3 deceq12i.2 . . 3 𝐶 = 𝐷
43deceq2i 9308 . 2 𝐵𝐶 = 𝐵𝐷
52, 4eqtri 2178 1 𝐴𝐶 = 𝐵𝐷
Colors of variables: wff set class
Syntax hints:   = wceq 1335  cdc 9301
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-v 2714  df-un 3106  df-sn 3567  df-pr 3568  df-op 3570  df-uni 3775  df-br 3968  df-iota 5138  df-fv 5181  df-ov 5830  df-dec 9302
This theorem is referenced by:  11multnc  9368
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