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Theorem deceq12i 10131
Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.)
Hypotheses
Ref Expression
deceq1i.1  |-  A  =  B
deceq12i.2  |-  C  =  D
Assertion
Ref Expression
deceq12i  |- ; A C  = ; B D

Proof of Theorem deceq12i
StepHypRef Expression
1 deceq1i.1 . . 3  |-  A  =  B
21deceq1i 10129 . 2  |- ; A C  = ; B C
3 deceq12i.2 . . 3  |-  C  =  D
43deceq2i 10130 . 2  |- ; B C  = ; B D
52, 4eqtri 2303 1  |- ; A C  = ; B D
Colors of variables: wff set class
Syntax hints:    = wceq 1623  ;cdc 10124
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861  df-dec 10125
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