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Theorem 5p3e8 9062
Description: 5 + 3 = 8. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
5p3e8  |-  ( 5  +  3 )  =  8

Proof of Theorem 5p3e8
StepHypRef Expression
1 df-3 8975 . . . 4  |-  3  =  ( 2  +  1 )
21oveq2i 5883 . . 3  |-  ( 5  +  3 )  =  ( 5  +  ( 2  +  1 ) )
3 5cn 8995 . . . 4  |-  5  e.  CC
4 2cn 8986 . . . 4  |-  2  e.  CC
5 ax-1cn 7901 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7962 . . 3  |-  ( ( 5  +  2 )  +  1 )  =  ( 5  +  ( 2  +  1 ) )
72, 6eqtr4i 2201 . 2  |-  ( 5  +  3 )  =  ( ( 5  +  2 )  +  1 )
8 df-8 8980 . . 3  |-  8  =  ( 7  +  1 )
9 5p2e7 9061 . . . 4  |-  ( 5  +  2 )  =  7
109oveq1i 5882 . . 3  |-  ( ( 5  +  2 )  +  1 )  =  ( 7  +  1 )
118, 10eqtr4i 2201 . 2  |-  8  =  ( ( 5  +  2 )  +  1 )
127, 11eqtr4i 2201 1  |-  ( 5  +  3 )  =  8
Colors of variables: wff set class
Syntax hints:    = wceq 1353  (class class class)co 5872   1c1 7809    + caddc 7811   2c2 8966   3c3 8967   5c5 8969   7c7 8971   8c8 8972
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-resscn 7900  ax-1cn 7901  ax-1re 7902  ax-addrcl 7905  ax-addass 7910
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-rex 2461  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3598  df-pr 3599  df-op 3601  df-uni 3810  df-br 4003  df-iota 5177  df-fv 5223  df-ov 5875  df-2 8974  df-3 8975  df-4 8976  df-5 8977  df-6 8978  df-7 8979  df-8 8980
This theorem is referenced by:  5p4e9  9063  ef01bndlem  11757  lgsdir2lem1  14300
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