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Theorem 2p2e4 10032
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 9992 . . 3  |-  2  =  ( 1  +  1 )
21oveq2i 6033 . 2  |-  ( 2  +  2 )  =  ( 2  +  ( 1  +  1 ) )
3 df-4 9994 . . 3  |-  4  =  ( 3  +  1 )
4 df-3 9993 . . . 4  |-  3  =  ( 2  +  1 )
54oveq1i 6032 . . 3  |-  ( 3  +  1 )  =  ( ( 2  +  1 )  +  1 )
6 2cn 10004 . . . 4  |-  2  e.  CC
7 ax-1cn 8983 . . . 4  |-  1  e.  CC
86, 7, 7addassi 9033 . . 3  |-  ( ( 2  +  1 )  +  1 )  =  ( 2  +  ( 1  +  1 ) )
93, 5, 83eqtri 2413 . 2  |-  4  =  ( 2  +  ( 1  +  1 ) )
102, 9eqtr4i 2412 1  |-  ( 2  +  2 )  =  4
Colors of variables: wff set class
Syntax hints:    = wceq 1649  (class class class)co 6022   1c1 8926    + caddc 8928   2c2 9983   3c3 9984   4c4 9985
This theorem is referenced by:  2t2e4  10061  i4  11412  ef01bndlem  12714  pythagtriplem1  13119  prmlem2  13371  43prm  13373  1259lem4  13382  2503lem1  13385  2503lem2  13386  2503lem3  13387  4001lem1  13389  4001lem4  13392  quart1lem  20564  log2ub  20658  4bc2eq6  24985  bpoly4  25821  fsumcube  25822  wallispi2lem1  27490  stirlinglem8  27500  2p2ne5  27884
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370  ax-resscn 8982  ax-1cn 8983  ax-icn 8984  ax-addcl 8985  ax-addrcl 8986  ax-mulcl 8987  ax-mulrcl 8988  ax-addass 8990  ax-i2m1 8993  ax-1ne0 8994  ax-rrecex 8997  ax-cnre 8998
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-ne 2554  df-ral 2656  df-rex 2657  df-rab 2660  df-v 2903  df-dif 3268  df-un 3270  df-in 3272  df-ss 3279  df-nul 3574  df-if 3685  df-sn 3765  df-pr 3766  df-op 3768  df-uni 3960  df-br 4156  df-iota 5360  df-fv 5404  df-ov 6025  df-2 9992  df-3 9993  df-4 9994
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