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Theorem deceq2i 10381
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 10379 . 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 1652  ;cdc 10375
This theorem is referenced by:  deceq12i  10382
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2704  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-uni 4009  df-br 4206  df-iota 5411  df-fv 5455  df-ov 6077  df-dec 10376
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