Theorem deceq1i 12099

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 12097	. 2 ⊢ (𝐴 = 𝐵 → ;𝐴𝐶 = ;𝐵𝐶)
3	1, 2	ax-mp 5	1 ⊢ ;𝐴𝐶 = ;𝐵𝐶

Syntax hints:   = wceq 1533  ;cdc 12092

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-rex 3144  df-rab 3147  df-v 3496  df-dif 3938  df-un 3940  df-in 3942  df-ss 3951  df-nul 4291  df-if 4467  df-sn 4561  df-pr 4563  df-op 4567  df-uni 4832  df-br 5059  df-iota 6308  df-fv 6357  df-ov 7153  df-dec 12093

This theorem is referenced by:  deceq12i  12101  decmul10add  12161  1mhdrd  30587  hgt750lem2  31918  sqn5ii  39165  fmtno5lem4  43712  fmtno5fac  43738