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Theorem 8p2e10 9885
Description: 8 + 2 = 10. (Contributed by NM, 5-Feb-2007.)
Assertion
Ref Expression
8p2e10  |-  ( 8  +  2 )  =  10

Proof of Theorem 8p2e10
StepHypRef Expression
1 df-2 9820 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5885 . . . 4  |-  ( 8  +  2 )  =  ( 8  +  ( 1  +  1 ) )
3 8re 9840 . . . . . 6  |-  8  e.  RR
43recni 8865 . . . . 5  |-  8  e.  CC
5 ax-1cn 8811 . . . . 5  |-  1  e.  CC
64, 5, 5addassi 8861 . . . 4  |-  ( ( 8  +  1 )  +  1 )  =  ( 8  +  ( 1  +  1 ) )
72, 6eqtr4i 2319 . . 3  |-  ( 8  +  2 )  =  ( ( 8  +  1 )  +  1 )
8 df-9 9827 . . . 4  |-  9  =  ( 8  +  1 )
98oveq1i 5884 . . 3  |-  ( 9  +  1 )  =  ( ( 8  +  1 )  +  1 )
107, 9eqtr4i 2319 . 2  |-  ( 8  +  2 )  =  ( 9  +  1 )
11 df-10 9828 . 2  |-  10  =  ( 9  +  1 )
1210, 11eqtr4i 2319 1  |-  ( 8  +  2 )  =  10
Colors of variables: wff set class
Syntax hints:    = wceq 1632  (class class class)co 5874   1c1 8754    + caddc 8756   2c2 9811   8c8 9817   9c9 9818   10c10 9819
This theorem is referenced by:  8p3e11  10196  8t5e40  10231  1259lem3  13147  1259lem4  13148  2503lem2  13152  4001lem1  13155  4001lem3  13157  4001prm  13159
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  df-10 9828
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