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Theorem 5p4e9 11794
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 11701 . . . 4 4 = (3 + 1)
21oveq2i 7162 . . 3 (5 + 4) = (5 + (3 + 1))
3 5cn 11724 . . . 4 5 ∈ ℂ
4 3cn 11717 . . . 4 3 ∈ ℂ
5 ax-1cn 10595 . . . 4 1 ∈ ℂ
63, 4, 5addassi 10651 . . 3 ((5 + 3) + 1) = (5 + (3 + 1))
72, 6eqtr4i 2850 . 2 (5 + 4) = ((5 + 3) + 1)
8 df-9 11706 . . 3 9 = (8 + 1)
9 5p3e8 11793 . . . 4 (5 + 3) = 8
109oveq1i 7161 . . 3 ((5 + 3) + 1) = (8 + 1)
118, 10eqtr4i 2850 . 2 9 = ((5 + 3) + 1)
127, 11eqtr4i 2850 1 (5 + 4) = 9
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  (class class class)co 7151  1c1 10538   + caddc 10540  3c3 11692  4c4 11693  5c5 11694  8c8 11697  9c9 11698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796  ax-1cn 10595  ax-addcl 10597  ax-addass 10602
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-un 3924  df-in 3926  df-ss 3936  df-sn 4551  df-pr 4553  df-op 4557  df-uni 4825  df-br 5054  df-iota 6304  df-fv 6353  df-ov 7154  df-2 11699  df-3 11700  df-4 11701  df-5 11702  df-6 11703  df-7 11704  df-8 11705  df-9 11706
This theorem is referenced by:  5p5e10  12168  139prm  16459  1259lem3  16468  1259lem4  16469  2503lem2  16473  4001lem1  16476  4001lem2  16477  hgt750lem2  32008  problem1  32993  problem2  32994  resqrtvalex  40289  imsqrtvalex  40290  inductionexd  40805  139prmALT  44066
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