Theorem dp2eq2i 31052

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

Hypothesis

Ref	Expression
dp2eq1i.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
dp2eq2i	⊢ _𝐶𝐴 = _𝐶𝐵

Proof of Theorem dp2eq2i

Step	Hyp	Ref	Expression
1		dp2eq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		dp2eq2 31050	. 2 ⊢ (𝐴 = 𝐵 → _𝐶𝐴 = _𝐶𝐵)
3	1, 2	ax-mp 5	1 ⊢ _𝐶𝐴 = _𝐶𝐵

Syntax hints:   = wceq 1539  _cdp2 31047

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3072  df-v 3424  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4254  df-if 4457  df-sn 4559  df-pr 4561  df-op 4565  df-uni 4837  df-br 5071  df-iota 6376  df-fv 6426  df-ov 7258  df-dp2 31048

This theorem is referenced by:  dp2eq12i  31053  hgt750lem2  32532