Theorem deceq12i 12723

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 12721	. 2 ⊢ ;𝐴𝐶 = ;𝐵𝐶
3		deceq12i.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	deceq2i 12722	. 2 ⊢ ;𝐵𝐶 = ;𝐵𝐷
5	2, 4	eqtri 2793	1 ⊢ ;𝐴𝐶 = ;𝐵𝐷

Syntax hints:   = wceq 1568  ;cdc 12714

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2152  ax-9 2160  ax-ext 2742

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1571  df-fal 1581  df-ex 1808  df-sb 2099  df-clab 2749  df-cleq 2762  df-clel 2845  df-rab 3424  df-v 3464  df-dif 3916  df-un 3918  df-ss 3930  df-nul 4295  df-if 4493  df-sn 4595  df-pr 4597  df-op 4601  df-uni 4878  df-br 5115  df-iota 6496  df-fv 6548  df-ov 7417  df-dec 12715

This theorem is referenced by:  11multnc  12787  2exp340mod341  48447