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Theorem 4p3e7 8055
Description: 4 + 3 = 7. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
4p3e7  |-  ( 4  +  3 )  =  7

Proof of Theorem 4p3e7
StepHypRef Expression
1 df-3 7974 . . . 4  |-  3  =  ( 2  +  1 )
21oveq2i 5523 . . 3  |-  ( 4  +  3 )  =  ( 4  +  ( 2  +  1 ) )
3 4cn 7993 . . . 4  |-  4  e.  CC
4 2cn 7986 . . . 4  |-  2  e.  CC
5 ax-1cn 6977 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7035 . . 3  |-  ( ( 4  +  2 )  +  1 )  =  ( 4  +  ( 2  +  1 ) )
72, 6eqtr4i 2063 . 2  |-  ( 4  +  3 )  =  ( ( 4  +  2 )  +  1 )
8 df-7 7978 . . 3  |-  7  =  ( 6  +  1 )
9 4p2e6 8054 . . . 4  |-  ( 4  +  2 )  =  6
109oveq1i 5522 . . 3  |-  ( ( 4  +  2 )  +  1 )  =  ( 6  +  1 )
118, 10eqtr4i 2063 . 2  |-  7  =  ( ( 4  +  2 )  +  1 )
127, 11eqtr4i 2063 1  |-  ( 4  +  3 )  =  7
Colors of variables: wff set class
Syntax hints:    = wceq 1243  (class class class)co 5512   1c1 6890    + caddc 6892   2c2 7964   3c3 7965   4c4 7966   6c6 7968   7c7 7969
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-resscn 6976  ax-1cn 6977  ax-1re 6978  ax-addrcl 6981  ax-addass 6986
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515  df-2 7973  df-3 7974  df-4 7975  df-5 7976  df-6 7977  df-7 7978
This theorem is referenced by:  4p4e8  8056
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