Theorem dp2eq12i 32805

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 32803	. 2 ⊢ _𝐴𝐶 = _𝐵𝐶
3		dp2eq12i.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	dp2eq2i 32804	. 2 ⊢ _𝐵𝐶 = _𝐵𝐷
5	2, 4	eqtri 2753	1 ⊢ _𝐴𝐶 = _𝐵𝐷

Syntax hints:   = wceq 1540  _cdp2 32799

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3412  df-v 3457  df-dif 3925  df-un 3927  df-ss 3939  df-nul 4305  df-if 4497  df-sn 4598  df-pr 4600  df-op 4604  df-uni 4880  df-br 5116  df-iota 6472  df-fv 6527  df-ov 7397  df-dp2 32800

This theorem is referenced by: (None)