Theorem dp2eq1i 32953

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 32951	. 2 ⊢ (𝐴 = 𝐵 → _𝐴𝐶 = _𝐵𝐶)
3	1, 2	ax-mp 5	1 ⊢ _𝐴𝐶 = _𝐵𝐶

Syntax hints:   = wceq 1542  _cdp2 32949

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-uni 4852  df-br 5087  df-iota 6450  df-fv 6502  df-ov 7365  df-dp2 32950

This theorem is referenced by:  dp2eq12i  32955