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

Step	Hyp	Ref	Expression
1		deceq1i.1	. . 3 ⊢ 𝐴 = 𝐵
2	1	deceq1i 12443	. 2 ⊢ ;𝐴𝐶 = ;𝐵𝐶
3		deceq12i.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	deceq2i 12444	. 2 ⊢ ;𝐵𝐶 = ;𝐵𝐷
5	2, 4	eqtri 2768	1 ⊢ ;𝐴𝐶 = ;𝐵𝐷

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