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Theorem 5p2e7 9063
Description: 5 + 2 = 7. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
5p2e7  |-  ( 5  +  2 )  =  7

Proof of Theorem 5p2e7
StepHypRef Expression
1 df-2 8976 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5885 . . . 4  |-  ( 5  +  2 )  =  ( 5  +  ( 1  +  1 ) )
3 5cn 8997 . . . . 5  |-  5  e.  CC
4 ax-1cn 7903 . . . . 5  |-  1  e.  CC
53, 4, 4addassi 7964 . . . 4  |-  ( ( 5  +  1 )  +  1 )  =  ( 5  +  ( 1  +  1 ) )
62, 5eqtr4i 2201 . . 3  |-  ( 5  +  2 )  =  ( ( 5  +  1 )  +  1 )
7 df-6 8980 . . . 4  |-  6  =  ( 5  +  1 )
87oveq1i 5884 . . 3  |-  ( 6  +  1 )  =  ( ( 5  +  1 )  +  1 )
96, 8eqtr4i 2201 . 2  |-  ( 5  +  2 )  =  ( 6  +  1 )
10 df-7 8981 . 2  |-  7  =  ( 6  +  1 )
119, 10eqtr4i 2201 1  |-  ( 5  +  2 )  =  7
Colors of variables: wff set class
Syntax hints:    = wceq 1353  (class class class)co 5874   1c1 7811    + caddc 7813   2c2 8968   5c5 8971   6c6 8972   7c7 8973
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 7902  ax-1cn 7903  ax-1re 7904  ax-addrcl 7907  ax-addass 7912
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 4004  df-iota 5178  df-fv 5224  df-ov 5877  df-2 8976  df-3 8977  df-4 8978  df-5 8979  df-6 8980  df-7 8981
This theorem is referenced by:  5p3e8  9064
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