Theorem deceq1i 12831

Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.)

Hypothesis

Ref	Expression
deceq1i.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
deceq1i	⊢ ;𝐴𝐶 = ;𝐵𝐶

Proof of Theorem deceq1i

Step	Hyp	Ref	Expression
1		deceq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		deceq1 12829	. 2 ⊢ (𝐴 = 𝐵 → ;𝐴𝐶 = ;𝐵𝐶)
3	1, 2	ax-mp 5	1 ⊢ ;𝐴𝐶 = ;𝐵𝐶

This proof depends on syntax axioms:   = wceq 1569  ;cdc 12824

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3416  df-v 3455  df-ss 3900  df-dif 4049  df-un 4153  df-nul 4281  df-if 4485  df-sn 4588  df-pr 4590  df-op 4838  df-uni 4870  df-br 5106  df-iota 6500  df-fv 6554  df-ov 7430  df-dec 12825

This theorem is used by:  deceq12i  12833  decmul10add  12898  1mhdrd  33535  hgt750lem2  35334  sqn5ii  43483  fmtno5lem4  48780  fmtno5fac  48806