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Theorem 2p2e4 9060
Description: Two plus two equals four. For more information, see "2+2=4 Trivia" on the Metamath Proof Explorer Home Page: https://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 8992 . . 3  |-  2  =  ( 1  +  1 )
21oveq2i 5899 . 2  |-  ( 2  +  2 )  =  ( 2  +  ( 1  +  1 ) )
3 df-4 8994 . . 3  |-  4  =  ( 3  +  1 )
4 df-3 8993 . . . 4  |-  3  =  ( 2  +  1 )
54oveq1i 5898 . . 3  |-  ( 3  +  1 )  =  ( ( 2  +  1 )  +  1 )
6 2cn 9004 . . . 4  |-  2  e.  CC
7 ax-1cn 7918 . . . 4  |-  1  e.  CC
86, 7, 7addassi 7979 . . 3  |-  ( ( 2  +  1 )  +  1 )  =  ( 2  +  ( 1  +  1 ) )
93, 5, 83eqtri 2212 . 2  |-  4  =  ( 2  +  ( 1  +  1 ) )
102, 9eqtr4i 2211 1  |-  ( 2  +  2 )  =  4
Colors of variables: wff set class
Syntax hints:    = wceq 1363  (class class class)co 5888   1c1 7826    + caddc 7828   2c2 8984   3c3 8985   4c4 8986
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169  ax-resscn 7917  ax-1cn 7918  ax-1re 7919  ax-addrcl 7922  ax-addass 7927
This theorem depends on definitions:  df-bi 117  df-3an 981  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-rex 2471  df-v 2751  df-un 3145  df-in 3147  df-ss 3154  df-sn 3610  df-pr 3611  df-op 3613  df-uni 3822  df-br 4016  df-iota 5190  df-fv 5236  df-ov 5891  df-2 8992  df-3 8993  df-4 8994
This theorem is referenced by:  2t2e4  9087  i4  10637  4bc2eq6  10768  resqrexlemover  11033  resqrexlemcalc1  11037  ef01bndlem  11778  6gcd4e2  12010  pythagtriplem1  12279
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