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Theorem deceq12i 10391
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 10389 . 2  |- ; A C  = ; B C
3 deceq12i.2 . . 3  |-  C  =  D
43deceq2i 10390 . 2  |- ; B C  = ; B D
52, 4eqtri 2458 1  |- ; A C  = ; B D
Colors of variables: wff set class
Syntax hints:    = wceq 1653  ;cdc 10384
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 2419
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 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-ov 6086  df-dec 10385
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