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Theorem 2p2e4 8533
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 8471 . . 3 2 = (1 + 1)
21oveq2i 5655 . 2 (2 + 2) = (2 + (1 + 1))
3 df-4 8473 . . 3 4 = (3 + 1)
4 df-3 8472 . . . 4 3 = (2 + 1)
54oveq1i 5654 . . 3 (3 + 1) = ((2 + 1) + 1)
6 2cn 8483 . . . 4 2 ∈ ℂ
7 ax-1cn 7428 . . . 4 1 ∈ ℂ
86, 7, 7addassi 7486 . . 3 ((2 + 1) + 1) = (2 + (1 + 1))
93, 5, 83eqtri 2112 . 2 4 = (2 + (1 + 1))
102, 9eqtr4i 2111 1 (2 + 2) = 4
Colors of variables: wff set class
Syntax hints:   = wceq 1289  (class class class)co 5644  1c1 7341   + caddc 7343  2c2 8463  3c3 8464  4c4 8465
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-resscn 7427  ax-1cn 7428  ax-1re 7429  ax-addrcl 7432  ax-addass 7437
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-sn 3450  df-pr 3451  df-op 3453  df-uni 3652  df-br 3844  df-iota 4975  df-fv 5018  df-ov 5647  df-2 8471  df-3 8472  df-4 8473
This theorem is referenced by:  2t2e4  8560  i4  10045  4bc2eq6  10170  resqrexlemover  10431  resqrexlemcalc1  10435  ef01bndlem  11034  6gcd4e2  11249
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