Theorem deceq12i 12648

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 12646	. 2 ⊢ ;𝐴𝐶 = ;𝐵𝐶
3		deceq12i.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	deceq2i 12647	. 2 ⊢ ;𝐵𝐶 = ;𝐵𝐷
5	2, 4	eqtri 2760	1 ⊢ ;𝐴𝐶 = ;𝐵𝐷

Syntax hints:   = wceq 1542  ;cdc 12639

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-uni 4852  df-br 5087  df-iota 6450  df-fv 6502  df-ov 7365  df-dec 12640

This theorem is referenced by:  11multnc  12707  2exp340mod341  48225