Theorem dp2eq12i 32841

Description: Equality theorem for the decimal expansion constructor. (Contributed by David A. Wheeler, 15-May-2015.)

Hypotheses

Ref	Expression
dp2eq1i.1	⊢ 𝐴 = 𝐵
dp2eq12i.2	⊢ 𝐶 = 𝐷

Assertion

Ref	Expression
dp2eq12i	⊢ _𝐴𝐶 = _𝐵𝐷

Proof of Theorem dp2eq12i

Step	Hyp	Ref	Expression
1		dp2eq1i.1	. . 3 ⊢ 𝐴 = 𝐵
2	1	dp2eq1i 32839	. 2 ⊢ _𝐴𝐶 = _𝐵𝐶
3		dp2eq12i.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	dp2eq2i 32840	. 2 ⊢ _𝐵𝐶 = _𝐵𝐷
5	2, 4	eqtri 2768	1 ⊢ _𝐴𝐶 = _𝐵𝐷

Syntax hints:   = wceq 1537  _cdp2 32835

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4353  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-uni 4932  df-br 5167  df-iota 6525  df-fv 6581  df-ov 7451  df-dp2 32836

This theorem is referenced by: (None)