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Theorem deceq12i 9351
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 9349 . 2 𝐴𝐶 = 𝐵𝐶
3 deceq12i.2 . . 3 𝐶 = 𝐷
43deceq2i 9350 . 2 𝐵𝐶 = 𝐵𝐷
52, 4eqtri 2191 1 𝐴𝐶 = 𝐵𝐷
Colors of variables: wff set class
Syntax hints:   = wceq 1348  cdc 9343
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-v 2732  df-un 3125  df-sn 3589  df-pr 3590  df-op 3592  df-uni 3797  df-br 3990  df-iota 5160  df-fv 5206  df-ov 5856  df-dec 9344
This theorem is referenced by:  11multnc  9410
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