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Theorem 4p2e6 8831
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 8747 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5753 . . . 4  |-  ( 4  +  2 )  =  ( 4  +  ( 1  +  1 ) )
3 4cn 8766 . . . . 5  |-  4  e.  CC
4 ax-1cn 7681 . . . . 5  |-  1  e.  CC
53, 4, 4addassi 7742 . . . 4  |-  ( ( 4  +  1 )  +  1 )  =  ( 4  +  ( 1  +  1 ) )
62, 5eqtr4i 2141 . . 3  |-  ( 4  +  2 )  =  ( ( 4  +  1 )  +  1 )
7 df-5 8750 . . . 4  |-  5  =  ( 4  +  1 )
87oveq1i 5752 . . 3  |-  ( 5  +  1 )  =  ( ( 4  +  1 )  +  1 )
96, 8eqtr4i 2141 . 2  |-  ( 4  +  2 )  =  ( 5  +  1 )
10 df-6 8751 . 2  |-  6  =  ( 5  +  1 )
119, 10eqtr4i 2141 1  |-  ( 4  +  2 )  =  6
Colors of variables: wff set class
Syntax hints:    = wceq 1316  (class class class)co 5742   1c1 7589    + caddc 7591   2c2 8739   4c4 8741   5c5 8742   6c6 8743
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-resscn 7680  ax-1cn 7681  ax-1re 7682  ax-addrcl 7685  ax-addass 7690
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-iota 5058  df-fv 5101  df-ov 5745  df-2 8747  df-3 8748  df-4 8749  df-5 8750  df-6 8751
This theorem is referenced by:  4p3e7  8832  div4p1lem1div2  8941  4t4e16  9248  6gcd4e2  11610
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