Theorem dp2eq2i 32789

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 32787	. 2 ⊢ (𝐴 = 𝐵 → _𝐶𝐴 = _𝐶𝐵)
3	1, 2	ax-mp 5	1 ⊢ _𝐶𝐴 = _𝐶𝐵

Syntax hints:   = wceq 1539  _cdp2 32784

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-rab 3420  df-v 3465  df-dif 3934  df-un 3936  df-ss 3948  df-nul 4314  df-if 4506  df-sn 4607  df-pr 4609  df-op 4613  df-uni 4888  df-br 5124  df-iota 6493  df-fv 6548  df-ov 7415  df-dp2 32785

This theorem is referenced by:  dp2eq12i  32790  hgt750lem2  34601