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Theorem 5p4e9 8131
Description: 5 + 4 = 9. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
5p4e9 (5 + 4) = 9

Proof of Theorem 5p4e9
StepHypRef Expression
1 df-4 8051 . . . 4 4 = (3 + 1)
21oveq2i 5551 . . 3 (5 + 4) = (5 + (3 + 1))
3 5cn 8070 . . . 4 5 ∈ ℂ
4 3cn 8065 . . . 4 3 ∈ ℂ
5 ax-1cn 7035 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7093 . . 3 ((5 + 3) + 1) = (5 + (3 + 1))
72, 6eqtr4i 2079 . 2 (5 + 4) = ((5 + 3) + 1)
8 df-9 8056 . . 3 9 = (8 + 1)
9 5p3e8 8130 . . . 4 (5 + 3) = 8
109oveq1i 5550 . . 3 ((5 + 3) + 1) = (8 + 1)
118, 10eqtr4i 2079 . 2 9 = ((5 + 3) + 1)
127, 11eqtr4i 2079 1 (5 + 4) = 9
Colors of variables: wff set class
Syntax hints:   = wceq 1259  (class class class)co 5540  1c1 6948   + caddc 6950  3c3 8041  4c4 8042  5c5 8043  8c8 8046  9c9 8047
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-resscn 7034  ax-1cn 7035  ax-1re 7036  ax-addrcl 7039  ax-addass 7044
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-rex 2329  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-br 3793  df-iota 4895  df-fv 4938  df-ov 5543  df-2 8049  df-3 8050  df-4 8051  df-5 8052  df-6 8053  df-7 8054  df-8 8055  df-9 8056
This theorem is referenced by:  5p5e10  8497
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