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Theorem 2p2e4 8699
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 8637 . . 3  |-  2  =  ( 1  +  1 )
21oveq2i 5717 . 2  |-  ( 2  +  2 )  =  ( 2  +  ( 1  +  1 ) )
3 df-4 8639 . . 3  |-  4  =  ( 3  +  1 )
4 df-3 8638 . . . 4  |-  3  =  ( 2  +  1 )
54oveq1i 5716 . . 3  |-  ( 3  +  1 )  =  ( ( 2  +  1 )  +  1 )
6 2cn 8649 . . . 4  |-  2  e.  CC
7 ax-1cn 7588 . . . 4  |-  1  e.  CC
86, 7, 7addassi 7646 . . 3  |-  ( ( 2  +  1 )  +  1 )  =  ( 2  +  ( 1  +  1 ) )
93, 5, 83eqtri 2124 . 2  |-  4  =  ( 2  +  ( 1  +  1 ) )
102, 9eqtr4i 2123 1  |-  ( 2  +  2 )  =  4
Colors of variables: wff set class
Syntax hints:    = wceq 1299  (class class class)co 5706   1c1 7501    + caddc 7503   2c2 8629   3c3 8630   4c4 8631
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-resscn 7587  ax-1cn 7588  ax-1re 7589  ax-addrcl 7592  ax-addass 7597
This theorem depends on definitions:  df-bi 116  df-3an 932  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-rex 2381  df-v 2643  df-un 3025  df-in 3027  df-ss 3034  df-sn 3480  df-pr 3481  df-op 3483  df-uni 3684  df-br 3876  df-iota 5024  df-fv 5067  df-ov 5709  df-2 8637  df-3 8638  df-4 8639
This theorem is referenced by:  2t2e4  8726  i4  10236  4bc2eq6  10361  resqrexlemover  10622  resqrexlemcalc1  10626  ef01bndlem  11261  6gcd4e2  11476
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