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Theorem 2p2e4 9838
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/mpegif/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 9800 . . 3  |-  2  =  ( 1  +  1 )
21oveq2i 5831 . 2  |-  ( 2  +  2 )  =  ( 2  +  ( 1  +  1 ) )
3 df-4 9802 . . 3  |-  4  =  ( 3  +  1 )
4 df-3 9801 . . . 4  |-  3  =  ( 2  +  1 )
54oveq1i 5830 . . 3  |-  ( 3  +  1 )  =  ( ( 2  +  1 )  +  1 )
6 2cn 9812 . . . 4  |-  2  e.  CC
7 ax-1cn 8791 . . . 4  |-  1  e.  CC
86, 7, 7addassi 8841 . . 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 1624  (class class class)co 5820   1c1 8734    + caddc 8736   2c2 9791   3c3 9792   4c4 9793
This theorem is referenced by:  2t2e4  9867  i4  11200  ef01bndlem  12459  pythagtriplem1  12864  prmlem2  13116  43prm  13118  1259lem4  13127  2503lem1  13130  2503lem2  13131  2503lem3  13132  4001lem1  13134  4001lem4  13137  quart1lem  20146  log2ub  20240  4bc2eq6  23503  bpoly4  24202  fsumcube  24203  wallispi2lem1  27220  stirlinglem8  27230  2p2ne5  27532
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868  ax-ext 2266  ax-resscn 8790  ax-1cn 8791  ax-icn 8792  ax-addcl 8793  ax-addrcl 8794  ax-mulcl 8795  ax-mulrcl 8796  ax-addass 8798  ax-i2m1 8801  ax-1ne0 8802  ax-rrecex 8805  ax-cnre 8806
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 938  df-tru 1312  df-ex 1530  df-nf 1533  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-opab 4080  df-xp 4695  df-cnv 4697  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-fv 5230  df-ov 5823  df-2 9800  df-3 9801  df-4 9802
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