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Theorem 2p2e4 9844
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 9806 . . 3  |-  2  =  ( 1  +  1 )
21oveq2i 5871 . 2  |-  ( 2  +  2 )  =  ( 2  +  ( 1  +  1 ) )
3 df-4 9808 . . 3  |-  4  =  ( 3  +  1 )
4 df-3 9807 . . . 4  |-  3  =  ( 2  +  1 )
54oveq1i 5870 . . 3  |-  ( 3  +  1 )  =  ( ( 2  +  1 )  +  1 )
6 2cn 9818 . . . 4  |-  2  e.  CC
7 ax-1cn 8797 . . . 4  |-  1  e.  CC
86, 7, 7addassi 8847 . . 3  |-  ( ( 2  +  1 )  +  1 )  =  ( 2  +  ( 1  +  1 ) )
93, 5, 83eqtri 2309 . 2  |-  4  =  ( 2  +  ( 1  +  1 ) )
102, 9eqtr4i 2308 1  |-  ( 2  +  2 )  =  4
Colors of variables: wff set class
Syntax hints:    = wceq 1625  (class class class)co 5860   1c1 8740    + caddc 8742   2c2 9797   3c3 9798   4c4 9799
This theorem is referenced by:  2t2e4  9873  i4  11207  ef01bndlem  12466  pythagtriplem1  12871  prmlem2  13123  43prm  13125  1259lem4  13134  2503lem1  13137  2503lem2  13138  2503lem3  13139  4001lem1  13141  4001lem4  13144  quart1lem  20153  log2ub  20247  4bc2eq6  24101  bpoly4  24796  fsumcube  24797  wallispi2lem1  27831  stirlinglem8  27841  2p2ne5  28274
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266  ax-resscn 8796  ax-1cn 8797  ax-icn 8798  ax-addcl 8799  ax-addrcl 8800  ax-mulcl 8801  ax-mulrcl 8802  ax-addass 8804  ax-i2m1 8807  ax-1ne0 8808  ax-rrecex 8811  ax-cnre 8812
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-ne 2450  df-ral 2550  df-rex 2551  df-rab 2554  df-v 2792  df-dif 3157  df-un 3159  df-in 3161  df-ss 3168  df-nul 3458  df-if 3568  df-sn 3648  df-pr 3649  df-op 3651  df-uni 3830  df-br 4026  df-iota 5221  df-fv 5265  df-ov 5863  df-2 9806  df-3 9807  df-4 9808
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