Theorem dp2eq1i 32855

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 32853	. 2 ⊢ (𝐴 = 𝐵 → _𝐴𝐶 = _𝐵𝐶)
3	1, 2	ax-mp 5	1 ⊢ _𝐴𝐶 = _𝐵𝐶

Syntax hints:   = wceq 1538  _cdp2 32851

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1541  df-fal 1551  df-ex 1778  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3435  df-v 3481  df-dif 3967  df-un 3969  df-ss 3981  df-nul 4341  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-uni 4914  df-br 5150  df-iota 6519  df-fv 6574  df-ov 7438  df-dp2 32852

This theorem is referenced by:  dp2eq12i  32857