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Theorem 2p2e4 8870
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 8802 . . 3  |-  2  =  ( 1  +  1 )
21oveq2i 5792 . 2  |-  ( 2  +  2 )  =  ( 2  +  ( 1  +  1 ) )
3 df-4 8804 . . 3  |-  4  =  ( 3  +  1 )
4 df-3 8803 . . . 4  |-  3  =  ( 2  +  1 )
54oveq1i 5791 . . 3  |-  ( 3  +  1 )  =  ( ( 2  +  1 )  +  1 )
6 2cn 8814 . . . 4  |-  2  e.  CC
7 ax-1cn 7736 . . . 4  |-  1  e.  CC
86, 7, 7addassi 7797 . . 3  |-  ( ( 2  +  1 )  +  1 )  =  ( 2  +  ( 1  +  1 ) )
93, 5, 83eqtri 2165 . 2  |-  4  =  ( 2  +  ( 1  +  1 ) )
102, 9eqtr4i 2164 1  |-  ( 2  +  2 )  =  4
Colors of variables: wff set class
Syntax hints:    = wceq 1332  (class class class)co 5781   1c1 7644    + caddc 7646   2c2 8794   3c3 8795   4c4 8796
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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-resscn 7735  ax-1cn 7736  ax-1re 7737  ax-addrcl 7740  ax-addass 7745
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2691  df-un 3079  df-in 3081  df-ss 3088  df-sn 3537  df-pr 3538  df-op 3540  df-uni 3744  df-br 3937  df-iota 5095  df-fv 5138  df-ov 5784  df-2 8802  df-3 8803  df-4 8804
This theorem is referenced by:  2t2e4  8897  i4  10425  4bc2eq6  10551  resqrexlemover  10813  resqrexlemcalc1  10817  ef01bndlem  11497  6gcd4e2  11717
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