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Theorem 2p2e4 9842
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 9804 . . 3  |-  2  =  ( 1  +  1 )
21oveq2i 5869 . 2  |-  ( 2  +  2 )  =  ( 2  +  ( 1  +  1 ) )
3 df-4 9806 . . 3  |-  4  =  ( 3  +  1 )
4 df-3 9805 . . . 4  |-  3  =  ( 2  +  1 )
54oveq1i 5868 . . 3  |-  ( 3  +  1 )  =  ( ( 2  +  1 )  +  1 )
6 2cn 9816 . . . 4  |-  2  e.  CC
7 ax-1cn 8795 . . . 4  |-  1  e.  CC
86, 7, 7addassi 8845 . . 3  |-  ( ( 2  +  1 )  +  1 )  =  ( 2  +  ( 1  +  1 ) )
93, 5, 83eqtri 2307 . 2  |-  4  =  ( 2  +  ( 1  +  1 ) )
102, 9eqtr4i 2306 1  |-  ( 2  +  2 )  =  4
Colors of variables: wff set class
Syntax hints:    = wceq 1623  (class class class)co 5858   1c1 8738    + caddc 8740   2c2 9795   3c3 9796   4c4 9797
This theorem is referenced by:  2t2e4  9871  i4  11205  ef01bndlem  12464  pythagtriplem1  12869  prmlem2  13121  43prm  13123  1259lem4  13132  2503lem1  13135  2503lem2  13136  2503lem3  13137  4001lem1  13139  4001lem4  13142  quart1lem  20151  log2ub  20245  4bc2eq6  24099  bpoly4  24794  fsumcube  24795  wallispi2lem1  27820  stirlinglem8  27830  2p2ne5  28260
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 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-resscn 8794  ax-1cn 8795  ax-icn 8796  ax-addcl 8797  ax-addrcl 8798  ax-mulcl 8799  ax-mulrcl 8800  ax-addass 8802  ax-i2m1 8805  ax-1ne0 8806  ax-rrecex 8809  ax-cnre 8810
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 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861  df-2 9804  df-3 9805  df-4 9806
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