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Theorem 4p2e6 9087
Description: 4 + 2 = 6. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
4p2e6 (4 + 2) = 6

Proof of Theorem 4p2e6
StepHypRef Expression
1 df-2 9003 . . . . 5 2 = (1 + 1)
21oveq2i 5903 . . . 4 (4 + 2) = (4 + (1 + 1))
3 4cn 9022 . . . . 5 4 ∈ ℂ
4 ax-1cn 7929 . . . . 5 1 ∈ ℂ
53, 4, 4addassi 7990 . . . 4 ((4 + 1) + 1) = (4 + (1 + 1))
62, 5eqtr4i 2213 . . 3 (4 + 2) = ((4 + 1) + 1)
7 df-5 9006 . . . 4 5 = (4 + 1)
87oveq1i 5902 . . 3 (5 + 1) = ((4 + 1) + 1)
96, 8eqtr4i 2213 . 2 (4 + 2) = (5 + 1)
10 df-6 9007 . 2 6 = (5 + 1)
119, 10eqtr4i 2213 1 (4 + 2) = 6
Colors of variables: wff set class
Syntax hints:   = wceq 1364  (class class class)co 5892  1c1 7837   + caddc 7839  2c2 8995  4c4 8997  5c5 8998  6c6 8999
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-resscn 7928  ax-1cn 7929  ax-1re 7930  ax-addrcl 7933  ax-addass 7938
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-br 4019  df-iota 5193  df-fv 5240  df-ov 5895  df-2 9003  df-3 9004  df-4 9005  df-5 9006  df-6 9007
This theorem is referenced by:  4p3e7  9088  div4p1lem1div2  9197  4t4e16  9507  6gcd4e2  12023
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