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Theorem 5p3e8 8058
Description: 5 + 3 = 8. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
5p3e8 (5 + 3) = 8

Proof of Theorem 5p3e8
StepHypRef Expression
1 df-3 7974 . . . 4 3 = (2 + 1)
21oveq2i 5523 . . 3 (5 + 3) = (5 + (2 + 1))
3 5cn 7995 . . . 4 5 ∈ ℂ
4 2cn 7986 . . . 4 2 ∈ ℂ
5 ax-1cn 6977 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7035 . . 3 ((5 + 2) + 1) = (5 + (2 + 1))
72, 6eqtr4i 2063 . 2 (5 + 3) = ((5 + 2) + 1)
8 df-8 7979 . . 3 8 = (7 + 1)
9 5p2e7 8057 . . . 4 (5 + 2) = 7
109oveq1i 5522 . . 3 ((5 + 2) + 1) = (7 + 1)
118, 10eqtr4i 2063 . 2 8 = ((5 + 2) + 1)
127, 11eqtr4i 2063 1 (5 + 3) = 8
Colors of variables: wff set class
Syntax hints:   = wceq 1243  (class class class)co 5512  1c1 6890   + caddc 6892  2c2 7964  3c3 7965  5c5 7967  7c7 7969  8c8 7970
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-resscn 6976  ax-1cn 6977  ax-1re 6978  ax-addrcl 6981  ax-addass 6986
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515  df-2 7973  df-3 7974  df-4 7975  df-5 7976  df-6 7977  df-7 7978  df-8 7979
This theorem is referenced by:  5p4e9  8059
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