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Theorem 7p3e10 8065
Description: 7 + 3 = 10. (Contributed by NM, 5-Feb-2007.)
Assertion
Ref Expression
7p3e10 (7 + 3) = 10

Proof of Theorem 7p3e10
StepHypRef Expression
1 df-3 7974 . . . 4 3 = (2 + 1)
21oveq2i 5523 . . 3 (7 + 3) = (7 + (2 + 1))
3 7cn 7999 . . . 4 7 ∈ ℂ
4 2cn 7986 . . . 4 2 ∈ ℂ
5 ax-1cn 6977 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7035 . . 3 ((7 + 2) + 1) = (7 + (2 + 1))
72, 6eqtr4i 2063 . 2 (7 + 3) = ((7 + 2) + 1)
8 df-10 7981 . . 3 10 = (9 + 1)
9 7p2e9 8064 . . . 4 (7 + 2) = 9
109oveq1i 5522 . . 3 ((7 + 2) + 1) = (9 + 1)
118, 10eqtr4i 2063 . 2 10 = ((7 + 2) + 1)
127, 11eqtr4i 2063 1 (7 + 3) = 10
Colors of variables: wff set class
Syntax hints:   = wceq 1243  (class class class)co 5512  1c1 6890   + caddc 6892  2c2 7964  3c3 7965  7c7 7969  9c9 7971  10c10 7972
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  df-9 7980  df-10 7981
This theorem is referenced by:  7p4e11  8419
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