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Theorem 4p3e7 8832
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 8748 . . . 4 3 = (2 + 1)
21oveq2i 5753 . . 3 (4 + 3) = (4 + (2 + 1))
3 4cn 8766 . . . 4 4 ∈ ℂ
4 2cn 8759 . . . 4 2 ∈ ℂ
5 ax-1cn 7681 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7742 . . 3 ((4 + 2) + 1) = (4 + (2 + 1))
72, 6eqtr4i 2141 . 2 (4 + 3) = ((4 + 2) + 1)
8 df-7 8752 . . 3 7 = (6 + 1)
9 4p2e6 8831 . . . 4 (4 + 2) = 6
109oveq1i 5752 . . 3 ((4 + 2) + 1) = (6 + 1)
118, 10eqtr4i 2141 . 2 7 = ((4 + 2) + 1)
127, 11eqtr4i 2141 1 (4 + 3) = 7
Colors of variables: wff set class
Syntax hints:   = wceq 1316  (class class class)co 5742  1c1 7589   + caddc 7591  2c2 8739  3c3 8740  4c4 8741  6c6 8743  7c7 8744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-resscn 7680  ax-1cn 7681  ax-1re 7682  ax-addrcl 7685  ax-addass 7690
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-iota 5058  df-fv 5101  df-ov 5745  df-2 8747  df-3 8748  df-4 8749  df-5 8750  df-6 8751  df-7 8752
This theorem is referenced by:  4p4e8  8833
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