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Theorem 4p4e8 8561
Description: 4 + 4 = 8. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
4p4e8 (4 + 4) = 8

Proof of Theorem 4p4e8
StepHypRef Expression
1 df-4 8483 . . . 4 4 = (3 + 1)
21oveq2i 5663 . . 3 (4 + 4) = (4 + (3 + 1))
3 4cn 8500 . . . 4 4 ∈ ℂ
4 3cn 8497 . . . 4 3 ∈ ℂ
5 ax-1cn 7438 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7496 . . 3 ((4 + 3) + 1) = (4 + (3 + 1))
72, 6eqtr4i 2111 . 2 (4 + 4) = ((4 + 3) + 1)
8 df-8 8487 . . 3 8 = (7 + 1)
9 4p3e7 8560 . . . 4 (4 + 3) = 7
109oveq1i 5662 . . 3 ((4 + 3) + 1) = (7 + 1)
118, 10eqtr4i 2111 . 2 8 = ((4 + 3) + 1)
127, 11eqtr4i 2111 1 (4 + 4) = 8
Colors of variables: wff set class
Syntax hints:   = wceq 1289  (class class class)co 5652  1c1 7351   + caddc 7353  3c3 8474  4c4 8475  7c7 8478  8c8 8479
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-resscn 7437  ax-1cn 7438  ax-1re 7439  ax-addrcl 7442  ax-addass 7447
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-sn 3452  df-pr 3453  df-op 3455  df-uni 3654  df-br 3846  df-iota 4980  df-fv 5023  df-ov 5655  df-2 8481  df-3 8482  df-4 8483  df-5 8484  df-6 8485  df-7 8486  df-8 8487
This theorem is referenced by:  4t2e8  8574
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