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Theorem 4p3e7 8621
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 8543 . . . 4  |-  3  =  ( 2  +  1 )
21oveq2i 5677 . . 3  |-  ( 4  +  3 )  =  ( 4  +  ( 2  +  1 ) )
3 4cn 8561 . . . 4  |-  4  e.  CC
4 2cn 8554 . . . 4  |-  2  e.  CC
5 ax-1cn 7499 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7557 . . 3  |-  ( ( 4  +  2 )  +  1 )  =  ( 4  +  ( 2  +  1 ) )
72, 6eqtr4i 2112 . 2  |-  ( 4  +  3 )  =  ( ( 4  +  2 )  +  1 )
8 df-7 8547 . . 3  |-  7  =  ( 6  +  1 )
9 4p2e6 8620 . . . 4  |-  ( 4  +  2 )  =  6
109oveq1i 5676 . . 3  |-  ( ( 4  +  2 )  +  1 )  =  ( 6  +  1 )
118, 10eqtr4i 2112 . 2  |-  7  =  ( ( 4  +  2 )  +  1 )
127, 11eqtr4i 2112 1  |-  ( 4  +  3 )  =  7
Colors of variables: wff set class
Syntax hints:    = wceq 1290  (class class class)co 5666   1c1 7412    + caddc 7414   2c2 8534   3c3 8535   4c4 8536   6c6 8538   7c7 8539
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-resscn 7498  ax-1cn 7499  ax-1re 7500  ax-addrcl 7503  ax-addass 7508
This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-rex 2366  df-v 2622  df-un 3004  df-in 3006  df-ss 3013  df-sn 3456  df-pr 3457  df-op 3459  df-uni 3660  df-br 3852  df-iota 4993  df-fv 5036  df-ov 5669  df-2 8542  df-3 8543  df-4 8544  df-5 8545  df-6 8546  df-7 8547
This theorem is referenced by:  4p4e8  8622
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