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Theorem deceq2i 10313
Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.)
Hypothesis
Ref Expression
deceq1i.1  |-  A  =  B
Assertion
Ref Expression
deceq2i  |- ; C A  = ; C B

Proof of Theorem deceq2i
StepHypRef Expression
1 deceq1i.1 . 2  |-  A  =  B
2 deceq2 10311 . 2  |-  ( A  =  B  -> ; C A  = ; C B )
31, 2ax-mp 8 1  |- ; C A  = ; C B
Colors of variables: wff set class
Syntax hints:    = wceq 1649  ;cdc 10307
This theorem is referenced by:  deceq12i  10314
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-uni 3951  df-br 4147  df-iota 5351  df-fv 5395  df-ov 6016  df-dec 10308
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