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Theorem deceq12i 12445
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 12443 . 2 𝐴𝐶 = 𝐵𝐶
3 deceq12i.2 . . 3 𝐶 = 𝐷
43deceq2i 12444 . 2 𝐵𝐶 = 𝐵𝐷
52, 4eqtri 2768 1 𝐴𝐶 = 𝐵𝐷
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cdc 12436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-ext 2711
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1545  df-fal 1555  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-clel 2818  df-rab 3075  df-v 3433  df-dif 3895  df-un 3897  df-in 3899  df-ss 3909  df-nul 4263  df-if 4466  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4846  df-br 5080  df-iota 6390  df-fv 6440  df-ov 7274  df-dec 12437
This theorem is referenced by:  11multnc  12504  2exp340mod341  45154
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