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Theorem 7p3e10 8501
Description: 7 + 3 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.)
Assertion
Ref Expression
7p3e10 (7 + 3) = 10

Proof of Theorem 7p3e10
StepHypRef Expression
1 df-3 8050 . . . 4 3 = (2 + 1)
21oveq2i 5551 . . 3 (7 + 3) = (7 + (2 + 1))
3 7cn 8074 . . . 4 7 ∈ ℂ
4 2cn 8061 . . . 4 2 ∈ ℂ
5 ax-1cn 7035 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7093 . . 3 ((7 + 2) + 1) = (7 + (2 + 1))
72, 6eqtr4i 2079 . 2 (7 + 3) = ((7 + 2) + 1)
8 7p2e9 8134 . . 3 (7 + 2) = 9
98oveq1i 5550 . 2 ((7 + 2) + 1) = (9 + 1)
10 9p1e10 8429 . 2 (9 + 1) = 10
117, 9, 103eqtri 2080 1 (7 + 3) = 10
Colors of variables: wff set class
Syntax hints:   = wceq 1259  (class class class)co 5540  0cc0 6947  1c1 6948   + caddc 6950  2c2 8040  3c3 8041  7c7 8045  9c9 8047  cdc 8427
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 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-cnex 7033  ax-resscn 7034  ax-1cn 7035  ax-1re 7036  ax-icn 7037  ax-addcl 7038  ax-addrcl 7039  ax-mulcl 7040  ax-mulcom 7043  ax-addass 7044  ax-mulass 7045  ax-distr 7046  ax-1rid 7049  ax-0id 7050  ax-cnre 7053
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-rab 2332  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-int 3644  df-br 3793  df-iota 4895  df-fv 4938  df-ov 5543  df-inn 7991  df-2 8049  df-3 8050  df-4 8051  df-5 8052  df-6 8053  df-7 8054  df-8 8055  df-9 8056  df-dec 8428
This theorem is referenced by:  7p4e11  8502
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