Theorem dp2eq2i 32846

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 32844	. 2 ⊢ (𝐴 = 𝐵 → _𝐶𝐴 = _𝐶𝐵)
3	1, 2	ax-mp 5	1 ⊢ _𝐶𝐴 = _𝐶𝐵

Syntax hints:   = wceq 1541  _cdp2 32841

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2112  ax-9 2120  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3394  df-v 3436  df-dif 3903  df-un 3905  df-ss 3917  df-nul 4282  df-if 4474  df-sn 4575  df-pr 4577  df-op 4581  df-uni 4858  df-br 5090  df-iota 6433  df-fv 6485  df-ov 7344  df-dp2 32842

This theorem is referenced by:  dp2eq12i  32847  hgt750lem2  34655