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Theorem 4p3e7 8127
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 8050 . . . 4  |-  3  =  ( 2  +  1 )
21oveq2i 5551 . . 3  |-  ( 4  +  3 )  =  ( 4  +  ( 2  +  1 ) )
3 4cn 8068 . . . 4  |-  4  e.  CC
4 2cn 8061 . . . 4  |-  2  e.  CC
5 ax-1cn 7035 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7093 . . 3  |-  ( ( 4  +  2 )  +  1 )  =  ( 4  +  ( 2  +  1 ) )
72, 6eqtr4i 2079 . 2  |-  ( 4  +  3 )  =  ( ( 4  +  2 )  +  1 )
8 df-7 8054 . . 3  |-  7  =  ( 6  +  1 )
9 4p2e6 8126 . . . 4  |-  ( 4  +  2 )  =  6
109oveq1i 5550 . . 3  |-  ( ( 4  +  2 )  +  1 )  =  ( 6  +  1 )
118, 10eqtr4i 2079 . 2  |-  7  =  ( ( 4  +  2 )  +  1 )
127, 11eqtr4i 2079 1  |-  ( 4  +  3 )  =  7
Colors of variables: wff set class
Syntax hints:    = wceq 1259  (class class class)co 5540   1c1 6948    + caddc 6950   2c2 8040   3c3 8041   4c4 8042   6c6 8044   7c7 8045
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-resscn 7034  ax-1cn 7035  ax-1re 7036  ax-addrcl 7039  ax-addass 7044
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-br 3793  df-iota 4895  df-fv 4938  df-ov 5543  df-2 8049  df-3 8050  df-4 8051  df-5 8052  df-6 8053  df-7 8054
This theorem is referenced by:  4p4e8  8128
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