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Theorem 2p2e4 7775
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 7713 . . 3 2 = (1 + 1)
21oveq2i 5466 . 2 (2 + 2) = (2 + (1 + 1))
3 df-4 7715 . . 3 4 = (3 + 1)
4 df-3 7714 . . . 4 3 = (2 + 1)
54oveq1i 5465 . . 3 (3 + 1) = ((2 + 1) + 1)
6 2cn 7726 . . . 4 2
7 ax-1cn 6736 . . . 4 1
86, 7, 7addassi 6793 . . 3 ((2 + 1) + 1) = (2 + (1 + 1))
93, 5, 83eqtri 2061 . 2 4 = (2 + (1 + 1))
102, 9eqtr4i 2060 1 (2 + 2) = 4
Colors of variables: wff set class
Syntax hints:   = wceq 1242  (class class class)co 5455  1c1 6672   + caddc 6674  2c2 7704  3c3 7705  4c4 7706
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-resscn 6735  ax-1cn 6736  ax-1re 6737  ax-addrcl 6740  ax-addass 6745
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458  df-2 7713  df-3 7714  df-4 7715
This theorem is referenced by:  2t2e4  7807  i4  8968
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