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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 2308 . 2  |-  4  =  ( 2  +  ( 1  +  1 ) )
102, 9eqtr4i 2307 1  |-  ( 2  +  2 )  =  4
Colors of variables: wff set class
Syntax hints:    = wceq 1623  (class class class)co 5820   1c1 8734    + caddc 8736   2c2 9791   3c3 9792   4c4 9793
This theorem is referenced by:  2t2e4  9867  i4  11201  ef01bndlem  12460  pythagtriplem1  12865  prmlem2  13117  43prm  13119  1259lem4  13128  2503lem1  13131  2503lem2  13132  2503lem3  13133  4001lem1  13135  4001lem4  13138  quart1lem  20147  log2ub  20241  4bc2eq6  23505  bpoly4  24204  fsumcube  24205  wallispi2lem1  27231  stirlinglem8  27241  2p2ne5  27543
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868  ax-ext 2265  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 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1631  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ne 2449  df-ral 2549  df-rex 2550  df-rab 2553  df-v 2791  df-dif 3156  df-un 3158  df-in 3160  df-ss 3167  df-nul 3457  df-if 3567  df-sn 3647  df-pr 3648  df-op 3650  df-uni 3829  df-br 4025  df-opab 4079  df-xp 4694  df-cnv 4696  df-dm 4698  df-rn 4699  df-res 4700  df-ima 4701  df-fv 5229  df-ov 5823  df-2 9800  df-3 9801  df-4 9802
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