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Theorem 6p3e9 9881
Description: 6 + 3 = 9. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
6p3e9  |-  ( 6  +  3 )  =  9

Proof of Theorem 6p3e9
StepHypRef Expression
1 df-3 9821 . . . 4  |-  3  =  ( 2  +  1 )
21oveq2i 5885 . . 3  |-  ( 6  +  3 )  =  ( 6  +  ( 2  +  1 ) )
3 6re 9838 . . . . 5  |-  6  e.  RR
43recni 8865 . . . 4  |-  6  e.  CC
5 2cn 9832 . . . 4  |-  2  e.  CC
6 ax-1cn 8811 . . . 4  |-  1  e.  CC
74, 5, 6addassi 8861 . . 3  |-  ( ( 6  +  2 )  +  1 )  =  ( 6  +  ( 2  +  1 ) )
82, 7eqtr4i 2319 . 2  |-  ( 6  +  3 )  =  ( ( 6  +  2 )  +  1 )
9 df-9 9827 . . 3  |-  9  =  ( 8  +  1 )
10 6p2e8 9880 . . . 4  |-  ( 6  +  2 )  =  8
1110oveq1i 5884 . . 3  |-  ( ( 6  +  2 )  +  1 )  =  ( 8  +  1 )
129, 11eqtr4i 2319 . 2  |-  9  =  ( ( 6  +  2 )  +  1 )
138, 12eqtr4i 2319 1  |-  ( 6  +  3 )  =  9
Colors of variables: wff set class
Syntax hints:    = wceq 1632  (class class class)co 5874   1c1 8754    + caddc 8756   2c2 9811   3c3 9812   6c6 9815   8c8 9817   9c9 9818
This theorem is referenced by:  6p4e10  9882  3t3e9  9889  2exp8  13118  139prm  13141  2503lem2  13152  4001lem1  13155  4001lem2  13156  4001lem4  13158  log2ublem3  20260  kur14lem8  23759
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-resscn 8810  ax-1cn 8811  ax-icn 8812  ax-addcl 8813  ax-addrcl 8814  ax-mulcl 8815  ax-mulrcl 8816  ax-addass 8818  ax-i2m1 8821  ax-1ne0 8822  ax-rrecex 8825  ax-cnre 8826
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877  df-2 9820  df-3 9821  df-4 9822  df-5 9823  df-6 9824  df-7 9825  df-8 9826  df-9 9827
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