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Theorem 2p2e4 9858
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 9820 . . 3  |-  2  =  ( 1  +  1 )
21oveq2i 5885 . 2  |-  ( 2  +  2 )  =  ( 2  +  ( 1  +  1 ) )
3 df-4 9822 . . 3  |-  4  =  ( 3  +  1 )
4 df-3 9821 . . . 4  |-  3  =  ( 2  +  1 )
54oveq1i 5884 . . 3  |-  ( 3  +  1 )  =  ( ( 2  +  1 )  +  1 )
6 2cn 9832 . . . 4  |-  2  e.  CC
7 ax-1cn 8811 . . . 4  |-  1  e.  CC
86, 7, 7addassi 8861 . . 3  |-  ( ( 2  +  1 )  +  1 )  =  ( 2  +  ( 1  +  1 ) )
93, 5, 83eqtri 2320 . 2  |-  4  =  ( 2  +  ( 1  +  1 ) )
102, 9eqtr4i 2319 1  |-  ( 2  +  2 )  =  4
Colors of variables: wff set class
Syntax hints:    = wceq 1632  (class class class)co 5874   1c1 8754    + caddc 8756   2c2 9811   3c3 9812   4c4 9813
This theorem is referenced by:  2t2e4  9887  i4  11221  ef01bndlem  12480  pythagtriplem1  12885  prmlem2  13137  43prm  13139  1259lem4  13148  2503lem1  13151  2503lem2  13152  2503lem3  13153  4001lem1  13155  4001lem4  13158  quart1lem  20167  log2ub  20261  4bc2eq6  24114  bpoly4  24866  fsumcube  24867  wallispi2lem1  27923  stirlinglem8  27933  2p2ne5  28517
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-resscn 8810  ax-1cn 8811  ax-icn 8812  ax-addcl 8813  ax-addrcl 8814  ax-mulcl 8815  ax-mulrcl 8816  ax-addass 8818  ax-i2m1 8821  ax-1ne0 8822  ax-rrecex 8825  ax-cnre 8826
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877  df-2 9820  df-3 9821  df-4 9822
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