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Theorem 2p2e4 8110
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 8049 . . 3 2 = (1 + 1)
21oveq2i 5551 . 2 (2 + 2) = (2 + (1 + 1))
3 df-4 8051 . . 3 4 = (3 + 1)
4 df-3 8050 . . . 4 3 = (2 + 1)
54oveq1i 5550 . . 3 (3 + 1) = ((2 + 1) + 1)
6 2cn 8061 . . . 4 2 ∈ ℂ
7 ax-1cn 7035 . . . 4 1 ∈ ℂ
86, 7, 7addassi 7093 . . 3 ((2 + 1) + 1) = (2 + (1 + 1))
93, 5, 83eqtri 2080 . 2 4 = (2 + (1 + 1))
102, 9eqtr4i 2079 1 (2 + 2) = 4
Colors of variables: wff set class
Syntax hints:   = wceq 1259  (class class class)co 5540  1c1 6948   + caddc 6950  2c2 8040  3c3 8041  4c4 8042
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-resscn 7034  ax-1cn 7035  ax-1re 7036  ax-addrcl 7039  ax-addass 7044
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-br 3793  df-iota 4895  df-fv 4938  df-ov 5543  df-2 8049  df-3 8050  df-4 8051
This theorem is referenced by:  2t2e4  8137  i4  9521  4bc2eq6  9642  resqrexlemover  9837  resqrexlemcalc1  9841
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