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Theorem 6p4e10 9431
Description: 6 + 4 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.)
Assertion
Ref Expression
6p4e10  |-  ( 6  +  4 )  = ; 1
0

Proof of Theorem 6p4e10
StepHypRef Expression
1 df-4 8956 . . . 4  |-  4  =  ( 3  +  1 )
21oveq2i 5879 . . 3  |-  ( 6  +  4 )  =  ( 6  +  ( 3  +  1 ) )
3 6cn 8977 . . . 4  |-  6  e.  CC
4 3cn 8970 . . . 4  |-  3  e.  CC
5 ax-1cn 7882 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7943 . . 3  |-  ( ( 6  +  3 )  +  1 )  =  ( 6  +  ( 3  +  1 ) )
72, 6eqtr4i 2201 . 2  |-  ( 6  +  4 )  =  ( ( 6  +  3 )  +  1 )
8 6p3e9 9045 . . 3  |-  ( 6  +  3 )  =  9
98oveq1i 5878 . 2  |-  ( ( 6  +  3 )  +  1 )  =  ( 9  +  1 )
10 9p1e10 9362 . 2  |-  ( 9  +  1 )  = ; 1
0
117, 9, 103eqtri 2202 1  |-  ( 6  +  4 )  = ; 1
0
Colors of variables: wff set class
Syntax hints:    = wceq 1353  (class class class)co 5868   0cc0 7789   1c1 7790    + caddc 7792   3c3 8947   4c4 8948   6c6 8950   9c9 8953  ;cdc 9360
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-sep 4118  ax-cnex 7880  ax-resscn 7881  ax-1cn 7882  ax-1re 7883  ax-icn 7884  ax-addcl 7885  ax-addrcl 7886  ax-mulcl 7887  ax-mulcom 7890  ax-addass 7891  ax-mulass 7892  ax-distr 7893  ax-1rid 7896  ax-0id 7897  ax-cnre 7900
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-rab 2464  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3597  df-pr 3598  df-op 3600  df-uni 3808  df-int 3843  df-br 4001  df-iota 5173  df-fv 5219  df-ov 5871  df-inn 8896  df-2 8954  df-3 8955  df-4 8956  df-5 8957  df-6 8958  df-7 8959  df-8 8960  df-9 8961  df-dec 9361
This theorem is referenced by:  6p5e11  9432  6t5e30  9466  ex-bc  14103
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