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Theorem 8p2e10 9958
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 9891 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5953 . . . 4  |-  ( 8  +  2 )  =  ( 8  +  ( 1  +  1 ) )
3 8re 9911 . . . . . 6  |-  8  e.  RR
43recni 8936 . . . . 5  |-  8  e.  CC
5 ax-1cn 8882 . . . . 5  |-  1  e.  CC
64, 5, 5addassi 8932 . . . 4  |-  ( ( 8  +  1 )  +  1 )  =  ( 8  +  ( 1  +  1 ) )
72, 6eqtr4i 2381 . . 3  |-  ( 8  +  2 )  =  ( ( 8  +  1 )  +  1 )
8 df-9 9898 . . . 4  |-  9  =  ( 8  +  1 )
98oveq1i 5952 . . 3  |-  ( 9  +  1 )  =  ( ( 8  +  1 )  +  1 )
107, 9eqtr4i 2381 . 2  |-  ( 8  +  2 )  =  ( 9  +  1 )
11 df-10 9899 . 2  |-  10  =  ( 9  +  1 )
1210, 11eqtr4i 2381 1  |-  ( 8  +  2 )  =  10
Colors of variables: wff set class
Syntax hints:    = wceq 1642  (class class class)co 5942   1c1 8825    + caddc 8827   2c2 9882   8c8 9888   9c9 9889   10c10 9890
This theorem is referenced by:  8p3e11  10269  8t5e40  10304  1259lem3  13222  1259lem4  13223  2503lem2  13227  4001lem1  13230  4001lem3  13232  4001prm  13234
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-resscn 8881  ax-1cn 8882  ax-icn 8883  ax-addcl 8884  ax-addrcl 8885  ax-mulcl 8886  ax-mulrcl 8887  ax-addass 8889  ax-i2m1 8892  ax-1ne0 8893  ax-rrecex 8896  ax-cnre 8897
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-uni 3907  df-br 4103  df-iota 5298  df-fv 5342  df-ov 5945  df-2 9891  df-3 9892  df-4 9893  df-5 9894  df-6 9895  df-7 9896  df-8 9897  df-9 9898  df-10 9899
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