Theorem dp2eq12i 31438

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 31436	. 2 ⊢ _𝐴𝐶 = _𝐵𝐶
3		dp2eq12i.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	dp2eq2i 31437	. 2 ⊢ _𝐵𝐶 = _𝐵𝐷
5	2, 4	eqtri 2764	1 ⊢ _𝐴𝐶 = _𝐵𝐷

Syntax hints:   = wceq 1540  _cdp2 31432

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3404  df-v 3443  df-dif 3901  df-un 3903  df-in 3905  df-ss 3915  df-nul 4270  df-if 4474  df-sn 4574  df-pr 4576  df-op 4580  df-uni 4853  df-br 5093  df-iota 6431  df-fv 6487  df-ov 7340  df-dp2 31433

This theorem is referenced by: (None)