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Theorem 3p2e5 8815
Description: 3 + 2 = 5. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
3p2e5  |-  ( 3  +  2 )  =  5

Proof of Theorem 3p2e5
StepHypRef Expression
1 df-2 8739 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5751 . . . 4  |-  ( 3  +  2 )  =  ( 3  +  ( 1  +  1 ) )
3 3cn 8755 . . . . 5  |-  3  e.  CC
4 ax-1cn 7677 . . . . 5  |-  1  e.  CC
53, 4, 4addassi 7738 . . . 4  |-  ( ( 3  +  1 )  +  1 )  =  ( 3  +  ( 1  +  1 ) )
62, 5eqtr4i 2139 . . 3  |-  ( 3  +  2 )  =  ( ( 3  +  1 )  +  1 )
7 df-4 8741 . . . 4  |-  4  =  ( 3  +  1 )
87oveq1i 5750 . . 3  |-  ( 4  +  1 )  =  ( ( 3  +  1 )  +  1 )
96, 8eqtr4i 2139 . 2  |-  ( 3  +  2 )  =  ( 4  +  1 )
10 df-5 8742 . 2  |-  5  =  ( 4  +  1 )
119, 10eqtr4i 2139 1  |-  ( 3  +  2 )  =  5
Colors of variables: wff set class
Syntax hints:    = wceq 1314  (class class class)co 5740   1c1 7585    + caddc 7587   2c2 8731   3c3 8732   4c4 8733   5c5 8734
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-resscn 7676  ax-1cn 7677  ax-1re 7678  ax-addrcl 7681  ax-addass 7686
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-sn 3501  df-pr 3502  df-op 3504  df-uni 3705  df-br 3898  df-iota 5056  df-fv 5099  df-ov 5743  df-2 8739  df-3 8740  df-4 8741  df-5 8742
This theorem is referenced by:  3p3e6  8816
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