Theorem dp2eq1i 33205

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
dp2eq1i	⊢ _𝐴𝐶 = _𝐵𝐶

Proof of Theorem dp2eq1i

Step	Hyp	Ref	Expression
1		dp2eq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		dp2eq1 33203	. 2 ⊢ (𝐴 = 𝐵 → _𝐴𝐶 = _𝐵𝐶)
3	1, 2	ax-mp 5	1 ⊢ _𝐴𝐶 = _𝐵𝐶

This proof depends on syntax axioms:   = wceq 1569  _cdp2 33201

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1104  df-tru 1572  df-fal 1582  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-rab 3416  df-v 3456  df-dif 3907  df-un 3909  df-ss 3921  df-nul 4286  df-if 4487  df-sn 4589  df-pr 4591  df-op 4595  df-uni 4872  df-br 5109  df-iota 6492  df-fv 6544  df-ov 7415  df-dp2 33202

This theorem is used by:  dp2eq12i  33207