Theorem deceq1i 12717

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 12715	. 2 ⊢ (𝐴 = 𝐵 → ;𝐴𝐶 = ;𝐵𝐶)
3	1, 2	ax-mp 5	1 ⊢ ;𝐴𝐶 = ;𝐵𝐶

Syntax hints:   = wceq 1567  ;cdc 12710

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1570  df-fal 1580  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-rab 3424  df-v 3465  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 4877  df-br 5114  df-iota 6493  df-fv 6545  df-ov 7414  df-dec 12711

This theorem is referenced by:  deceq12i  12719  decmul10add  12784  1mhdrd  33175  hgt750lem2  34983  sqn5ii  42936  fmtno5lem4  48196  fmtno5fac  48222