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Theorem 5p4e9 8819
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 8738 . . . 4 4 = (3 + 1)
21oveq2i 5751 . . 3 (5 + 4) = (5 + (3 + 1))
3 5cn 8757 . . . 4 5 ∈ ℂ
4 3cn 8752 . . . 4 3 ∈ ℂ
5 ax-1cn 7677 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7738 . . 3 ((5 + 3) + 1) = (5 + (3 + 1))
72, 6eqtr4i 2139 . 2 (5 + 4) = ((5 + 3) + 1)
8 df-9 8743 . . 3 9 = (8 + 1)
9 5p3e8 8818 . . . 4 (5 + 3) = 8
109oveq1i 5750 . . 3 ((5 + 3) + 1) = (8 + 1)
118, 10eqtr4i 2139 . 2 9 = ((5 + 3) + 1)
127, 11eqtr4i 2139 1 (5 + 4) = 9
Colors of variables: wff set class
Syntax hints:   = wceq 1314  (class class class)co 5740  1c1 7585   + caddc 7587  3c3 8729  4c4 8730  5c5 8731  8c8 8734  9c9 8735
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-resscn 7676  ax-1cn 7677  ax-1re 7678  ax-addrcl 7681  ax-addass 7686
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-sn 3501  df-pr 3502  df-op 3504  df-uni 3705  df-br 3898  df-iota 5056  df-fv 5099  df-ov 5743  df-2 8736  df-3 8737  df-4 8738  df-5 8739  df-6 8740  df-7 8741  df-8 8742  df-9 8743
This theorem is referenced by:  5p5e10  9203
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