Theorem dp2eq12i 32936

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 32934	. 2 ⊢ _𝐴𝐶 = _𝐵𝐶
3		dp2eq12i.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	dp2eq2i 32935	. 2 ⊢ _𝐵𝐶 = _𝐵𝐷
5	2, 4	eqtri 2759	1 ⊢ _𝐴𝐶 = _𝐵𝐷

Syntax hints:   = wceq 1542  _cdp2 32930

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3390  df-v 3431  df-dif 3892  df-un 3894  df-ss 3906  df-nul 4274  df-if 4467  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4851  df-br 5086  df-iota 6454  df-fv 6506  df-ov 7370  df-dp2 32931

This theorem is referenced by: (None)