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Theorem 2p2e4 9005
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 8937 . . 3  |-  2  =  ( 1  +  1 )
21oveq2i 5864 . 2  |-  ( 2  +  2 )  =  ( 2  +  ( 1  +  1 ) )
3 df-4 8939 . . 3  |-  4  =  ( 3  +  1 )
4 df-3 8938 . . . 4  |-  3  =  ( 2  +  1 )
54oveq1i 5863 . . 3  |-  ( 3  +  1 )  =  ( ( 2  +  1 )  +  1 )
6 2cn 8949 . . . 4  |-  2  e.  CC
7 ax-1cn 7867 . . . 4  |-  1  e.  CC
86, 7, 7addassi 7928 . . 3  |-  ( ( 2  +  1 )  +  1 )  =  ( 2  +  ( 1  +  1 ) )
93, 5, 83eqtri 2195 . 2  |-  4  =  ( 2  +  ( 1  +  1 ) )
102, 9eqtr4i 2194 1  |-  ( 2  +  2 )  =  4
Colors of variables: wff set class
Syntax hints:    = wceq 1348  (class class class)co 5853   1c1 7775    + caddc 7777   2c2 8929   3c3 8930   4c4 8931
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152  ax-resscn 7866  ax-1cn 7867  ax-1re 7868  ax-addrcl 7871  ax-addass 7876
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-sn 3589  df-pr 3590  df-op 3592  df-uni 3797  df-br 3990  df-iota 5160  df-fv 5206  df-ov 5856  df-2 8937  df-3 8938  df-4 8939
This theorem is referenced by:  2t2e4  9032  i4  10578  4bc2eq6  10708  resqrexlemover  10974  resqrexlemcalc1  10978  ef01bndlem  11719  6gcd4e2  11950  pythagtriplem1  12219
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