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Theorem deceq1i 10388
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  |- ; A C  = ; B C

Proof of Theorem deceq1i
StepHypRef Expression
1 deceq1i.1 . 2  |-  A  =  B
2 deceq1 10386 . 2  |-  ( A  =  B  -> ; A C  = ; B C )
31, 2ax-mp 8 1  |- ; A C  = ; B C
Colors of variables: wff set class
Syntax hints:    = wceq 1653  ;cdc 10383
This theorem is referenced by:  deceq12i  10390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-rex 2712  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-iota 5419  df-fv 5463  df-ov 6085  df-dec 10384
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