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Theorem 5p4e9 8982
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 8895 . . . 4 4 = (3 + 1)
21oveq2i 5836 . . 3 (5 + 4) = (5 + (3 + 1))
3 5cn 8914 . . . 4 5 ∈ ℂ
4 3cn 8909 . . . 4 3 ∈ ℂ
5 ax-1cn 7826 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7887 . . 3 ((5 + 3) + 1) = (5 + (3 + 1))
72, 6eqtr4i 2181 . 2 (5 + 4) = ((5 + 3) + 1)
8 df-9 8900 . . 3 9 = (8 + 1)
9 5p3e8 8981 . . . 4 (5 + 3) = 8
109oveq1i 5835 . . 3 ((5 + 3) + 1) = (8 + 1)
118, 10eqtr4i 2181 . 2 9 = ((5 + 3) + 1)
127, 11eqtr4i 2181 1 (5 + 4) = 9
Colors of variables: wff set class
Syntax hints:   = wceq 1335  (class class class)co 5825  1c1 7734   + caddc 7736  3c3 8886  4c4 8887  5c5 8888  8c8 8891  9c9 8892
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-resscn 7825  ax-1cn 7826  ax-1re 7827  ax-addrcl 7830  ax-addass 7835
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-sn 3566  df-pr 3567  df-op 3569  df-uni 3774  df-br 3967  df-iota 5136  df-fv 5179  df-ov 5828  df-2 8893  df-3 8894  df-4 8895  df-5 8896  df-6 8897  df-7 8898  df-8 8899  df-9 8900
This theorem is referenced by:  5p5e10  9366
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