Theorem dp2eq2i 33165

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 33163	. 2 ⊢ (𝐴 = 𝐵 → _𝐶𝐴 = _𝐶𝐵)
3	1, 2	ax-mp 5	1 ⊢ _𝐶𝐴 = _𝐶𝐵

Syntax hints:   = wceq 1568  _cdp2 33160

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2152  ax-9 2160  ax-ext 2742

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1571  df-fal 1581  df-ex 1808  df-sb 2099  df-clab 2749  df-cleq 2762  df-clel 2845  df-rab 3424  df-v 3464  df-dif 3916  df-un 3918  df-ss 3930  df-nul 4295  df-if 4493  df-sn 4595  df-pr 4597  df-op 4601  df-uni 4878  df-br 5115  df-iota 6496  df-fv 6548  df-ov 7417  df-dp2 33161

This theorem is referenced by:  dp2eq12i  33166  hgt750lem2  35009