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Theorem 4p2e6 9092
Description: 4 + 2 = 6. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
4p2e6  |-  ( 4  +  2 )  =  6

Proof of Theorem 4p2e6
StepHypRef Expression
1 df-2 9008 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5907 . . . 4  |-  ( 4  +  2 )  =  ( 4  +  ( 1  +  1 ) )
3 4cn 9027 . . . . 5  |-  4  e.  CC
4 ax-1cn 7934 . . . . 5  |-  1  e.  CC
53, 4, 4addassi 7995 . . . 4  |-  ( ( 4  +  1 )  +  1 )  =  ( 4  +  ( 1  +  1 ) )
62, 5eqtr4i 2213 . . 3  |-  ( 4  +  2 )  =  ( ( 4  +  1 )  +  1 )
7 df-5 9011 . . . 4  |-  5  =  ( 4  +  1 )
87oveq1i 5906 . . 3  |-  ( 5  +  1 )  =  ( ( 4  +  1 )  +  1 )
96, 8eqtr4i 2213 . 2  |-  ( 4  +  2 )  =  ( 5  +  1 )
10 df-6 9012 . 2  |-  6  =  ( 5  +  1 )
119, 10eqtr4i 2213 1  |-  ( 4  +  2 )  =  6
Colors of variables: wff set class
Syntax hints:    = wceq 1364  (class class class)co 5896   1c1 7842    + caddc 7844   2c2 9000   4c4 9002   5c5 9003   6c6 9004
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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-resscn 7933  ax-1cn 7934  ax-1re 7935  ax-addrcl 7938  ax-addass 7943
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-br 4019  df-iota 5196  df-fv 5243  df-ov 5899  df-2 9008  df-3 9009  df-4 9010  df-5 9011  df-6 9012
This theorem is referenced by:  4p3e7  9093  div4p1lem1div2  9202  4t4e16  9512  6gcd4e2  12028
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