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Theorem 7p2e9 9046
Description: 7 + 2 = 9. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
7p2e9  |-  ( 7  +  2 )  =  9

Proof of Theorem 7p2e9
StepHypRef Expression
1 df-2 8954 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5879 . . . 4  |-  ( 7  +  2 )  =  ( 7  +  ( 1  +  1 ) )
3 7cn 8979 . . . . 5  |-  7  e.  CC
4 ax-1cn 7882 . . . . 5  |-  1  e.  CC
53, 4, 4addassi 7943 . . . 4  |-  ( ( 7  +  1 )  +  1 )  =  ( 7  +  ( 1  +  1 ) )
62, 5eqtr4i 2201 . . 3  |-  ( 7  +  2 )  =  ( ( 7  +  1 )  +  1 )
7 df-8 8960 . . . 4  |-  8  =  ( 7  +  1 )
87oveq1i 5878 . . 3  |-  ( 8  +  1 )  =  ( ( 7  +  1 )  +  1 )
96, 8eqtr4i 2201 . 2  |-  ( 7  +  2 )  =  ( 8  +  1 )
10 df-9 8961 . 2  |-  9  =  ( 8  +  1 )
119, 10eqtr4i 2201 1  |-  ( 7  +  2 )  =  9
Colors of variables: wff set class
Syntax hints:    = wceq 1353  (class class class)co 5868   1c1 7790    + caddc 7792   2c2 8946   7c7 8951   8c8 8952   9c9 8953
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 7881  ax-1cn 7882  ax-1re 7883  ax-addrcl 7886  ax-addass 7891
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 3597  df-pr 3598  df-op 3600  df-uni 3808  df-br 4001  df-iota 5173  df-fv 5219  df-ov 5871  df-2 8954  df-3 8955  df-4 8956  df-5 8957  df-6 8958  df-7 8959  df-8 8960  df-9 8961
This theorem is referenced by:  7p3e10  9434  7t7e49  9473  cos2bnd  11739
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