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Theorem 5p5e10 9485
Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.)
Assertion
Ref Expression
5p5e10  |-  ( 5  +  5 )  = ; 1
0

Proof of Theorem 5p5e10
StepHypRef Expression
1 df-5 9012 . . . 4  |-  5  =  ( 4  +  1 )
21oveq2i 5908 . . 3  |-  ( 5  +  5 )  =  ( 5  +  ( 4  +  1 ) )
3 5cn 9030 . . . 4  |-  5  e.  CC
4 4cn 9028 . . . 4  |-  4  e.  CC
5 ax-1cn 7935 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7996 . . 3  |-  ( ( 5  +  4 )  +  1 )  =  ( 5  +  ( 4  +  1 ) )
72, 6eqtr4i 2213 . 2  |-  ( 5  +  5 )  =  ( ( 5  +  4 )  +  1 )
8 5p4e9 9098 . . 3  |-  ( 5  +  4 )  =  9
98oveq1i 5907 . 2  |-  ( ( 5  +  4 )  +  1 )  =  ( 9  +  1 )
10 9p1e10 9417 . 2  |-  ( 9  +  1 )  = ; 1
0
117, 9, 103eqtri 2214 1  |-  ( 5  +  5 )  = ; 1
0
Colors of variables: wff set class
Syntax hints:    = wceq 1364  (class class class)co 5897   0cc0 7842   1c1 7843    + caddc 7845   4c4 9003   5c5 9004   9c9 9008  ;cdc 9415
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-sep 4136  ax-cnex 7933  ax-resscn 7934  ax-1cn 7935  ax-1re 7936  ax-icn 7937  ax-addcl 7938  ax-addrcl 7939  ax-mulcl 7940  ax-mulcom 7943  ax-addass 7944  ax-mulass 7945  ax-distr 7946  ax-1rid 7949  ax-0id 7950  ax-cnre 7953
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-rab 2477  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-int 3860  df-br 4019  df-iota 5196  df-fv 5243  df-ov 5900  df-inn 8951  df-2 9009  df-3 9010  df-4 9011  df-5 9012  df-6 9013  df-7 9014  df-8 9015  df-9 9016  df-dec 9416
This theorem is referenced by:  5t2e10  9514  5t4e20  9516
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