Theorem deceq1i 12683

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 12681	. 2 ⊢ (𝐴 = 𝐵 → ;𝐴𝐶 = ;𝐵𝐶)
3	1, 2	ax-mp 5	1 ⊢ ;𝐴𝐶 = ;𝐵𝐶

Syntax hints:   = wceq 1541  ;cdc 12676

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rab 3433  df-v 3476  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-uni 4909  df-br 5149  df-iota 6495  df-fv 6551  df-ov 7411  df-dec 12677

This theorem is referenced by:  deceq12i  12685  decmul10add  12745  1mhdrd  32077  hgt750lem2  33659  sqn5ii  41200  fmtno5lem4  46214  fmtno5fac  46240