Theorem dp2eq12i 31151

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 31149	. 2 ⊢ _𝐴𝐶 = _𝐵𝐶
3		dp2eq12i.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	dp2eq2i 31150	. 2 ⊢ _𝐵𝐶 = _𝐵𝐷
5	2, 4	eqtri 2766	1 ⊢ _𝐴𝐶 = _𝐵𝐷

Syntax hints:   = wceq 1539  _cdp2 31145

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-uni 4840  df-br 5075  df-iota 6391  df-fv 6441  df-ov 7278  df-dp2 31146

This theorem is referenced by: (None)