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Theorem 4p3e7 8097
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 8020 . . . 4 3 = (2 + 1)
21oveq2i 5548 . . 3 (4 + 3) = (4 + (2 + 1))
3 4cn 8038 . . . 4 4 ∈ ℂ
4 2cn 8031 . . . 4 2 ∈ ℂ
5 ax-1cn 7005 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7063 . . 3 ((4 + 2) + 1) = (4 + (2 + 1))
72, 6eqtr4i 2077 . 2 (4 + 3) = ((4 + 2) + 1)
8 df-7 8024 . . 3 7 = (6 + 1)
9 4p2e6 8096 . . . 4 (4 + 2) = 6
109oveq1i 5547 . . 3 ((4 + 2) + 1) = (6 + 1)
118, 10eqtr4i 2077 . 2 7 = ((4 + 2) + 1)
127, 11eqtr4i 2077 1 (4 + 3) = 7
Colors of variables: wff set class
Syntax hints:   = wceq 1257  (class class class)co 5537  1c1 6918   + caddc 6920  2c2 8010  3c3 8011  4c4 8012  6c6 8014  7c7 8015
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 638  ax-5 1350  ax-7 1351  ax-gen 1352  ax-ie1 1396  ax-ie2 1397  ax-8 1409  ax-10 1410  ax-11 1411  ax-i12 1412  ax-bndl 1413  ax-4 1414  ax-17 1433  ax-i9 1437  ax-ial 1441  ax-i5r 1442  ax-ext 2036  ax-resscn 7004  ax-1cn 7005  ax-1re 7006  ax-addrcl 7009  ax-addass 7014
This theorem depends on definitions:  df-bi 114  df-3an 896  df-tru 1260  df-nf 1364  df-sb 1660  df-clab 2041  df-cleq 2047  df-clel 2050  df-nfc 2181  df-rex 2327  df-v 2574  df-un 2947  df-in 2949  df-ss 2956  df-sn 3406  df-pr 3407  df-op 3409  df-uni 3606  df-br 3790  df-iota 4892  df-fv 4935  df-ov 5540  df-2 8019  df-3 8020  df-4 8021  df-5 8022  df-6 8023  df-7 8024
This theorem is referenced by:  4p4e8  8098
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