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Theorem 3p3e6 9092
Description: 3 + 3 = 6. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
3p3e6 (3 + 3) = 6

Proof of Theorem 3p3e6
StepHypRef Expression
1 df-3 9010 . . . 4 3 = (2 + 1)
21oveq2i 5908 . . 3 (3 + 3) = (3 + (2 + 1))
3 3cn 9025 . . . 4 3 ∈ ℂ
4 2cn 9021 . . . 4 2 ∈ ℂ
5 ax-1cn 7935 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7996 . . 3 ((3 + 2) + 1) = (3 + (2 + 1))
72, 6eqtr4i 2213 . 2 (3 + 3) = ((3 + 2) + 1)
8 df-6 9013 . . 3 6 = (5 + 1)
9 3p2e5 9091 . . . 4 (3 + 2) = 5
109oveq1i 5907 . . 3 ((3 + 2) + 1) = (5 + 1)
118, 10eqtr4i 2213 . 2 6 = ((3 + 2) + 1)
127, 11eqtr4i 2213 1 (3 + 3) = 6
Colors of variables: wff set class
Syntax hints:   = wceq 1364  (class class class)co 5897  1c1 7843   + caddc 7845  2c2 9001  3c3 9002  5c5 9004  6c6 9005
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 7934  ax-1cn 7935  ax-1re 7936  ax-addrcl 7939  ax-addass 7944
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 5196  df-fv 5243  df-ov 5900  df-2 9009  df-3 9010  df-4 9011  df-5 9012  df-6 9013
This theorem is referenced by:  3t2e6  9106  binom4  14874  ex-dvds  14960  ex-gcd  14961
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