Theorem deceq1i 12651

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 12649	. 2 ⊢ (𝐴 = 𝐵 → ;𝐴𝐶 = ;𝐵𝐶)
3	1, 2	ax-mp 5	1 ⊢ ;𝐴𝐶 = ;𝐵𝐶

Syntax hints:   = wceq 1542  ;cdc 12644

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 2708

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 2715  df-cleq 2728  df-clel 2811  df-rab 3390  df-v 3431  df-dif 3892  df-un 3894  df-ss 3906  df-nul 4274  df-if 4467  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4851  df-br 5086  df-iota 6454  df-fv 6506  df-ov 7370  df-dec 12645

This theorem is referenced by:  deceq12i  12653  decmul10add  12713  1mhdrd  32975  hgt750lem2  34796  sqn5ii  42718  fmtno5lem4  48019  fmtno5fac  48045