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Theorem 2p2e4 8037
 Description: Two plus two equals four. For more information, see "2+2=4 Trivia" on the Metamath Proof Explorer Home Page: http://us.metamath.org/mpeuni/mmset.html#trivia. (Contributed by NM, 27-May-1999.)
Assertion
Ref Expression
2p2e4 (2 + 2) = 4

Proof of Theorem 2p2e4
StepHypRef Expression
1 df-2 7973 . . 3 2 = (1 + 1)
21oveq2i 5523 . 2 (2 + 2) = (2 + (1 + 1))
3 df-4 7975 . . 3 4 = (3 + 1)
4 df-3 7974 . . . 4 3 = (2 + 1)
54oveq1i 5522 . . 3 (3 + 1) = ((2 + 1) + 1)
6 2cn 7986 . . . 4 2 ∈ ℂ
7 ax-1cn 6977 . . . 4 1 ∈ ℂ
86, 7, 7addassi 7035 . . 3 ((2 + 1) + 1) = (2 + (1 + 1))
93, 5, 83eqtri 2064 . 2 4 = (2 + (1 + 1))
102, 9eqtr4i 2063 1 (2 + 2) = 4
 Colors of variables: wff set class Syntax hints:   = wceq 1243  (class class class)co 5512  1c1 6890   + caddc 6892  2c2 7964  3c3 7965  4c4 7966 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-resscn 6976  ax-1cn 6977  ax-1re 6978  ax-addrcl 6981  ax-addass 6986 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515  df-2 7973  df-3 7974  df-4 7975 This theorem is referenced by:  2t2e4  8069  i4  9355  resqrexlemover  9608  resqrexlemcalc1  9612
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