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Theorem 8p2e10 9869
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 9804 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5869 . . . 4  |-  ( 8  +  2 )  =  ( 8  +  ( 1  +  1 ) )
3 8re 9824 . . . . . 6  |-  8  e.  RR
43recni 8849 . . . . 5  |-  8  e.  CC
5 ax-1cn 8795 . . . . 5  |-  1  e.  CC
64, 5, 5addassi 8845 . . . 4  |-  ( ( 8  +  1 )  +  1 )  =  ( 8  +  ( 1  +  1 ) )
72, 6eqtr4i 2306 . . 3  |-  ( 8  +  2 )  =  ( ( 8  +  1 )  +  1 )
8 df-9 9811 . . . 4  |-  9  =  ( 8  +  1 )
98oveq1i 5868 . . 3  |-  ( 9  +  1 )  =  ( ( 8  +  1 )  +  1 )
107, 9eqtr4i 2306 . 2  |-  ( 8  +  2 )  =  ( 9  +  1 )
11 df-10 9812 . 2  |-  10  =  ( 9  +  1 )
1210, 11eqtr4i 2306 1  |-  ( 8  +  2 )  =  10
Colors of variables: wff set class
Syntax hints:    = wceq 1623  (class class class)co 5858   1c1 8738    + caddc 8740   2c2 9795   8c8 9801   9c9 9802   10c10 9803
This theorem is referenced by:  8p3e11  10180  8t5e40  10215  1259lem3  13131  1259lem4  13132  2503lem2  13136  4001lem1  13139  4001lem3  13141  4001prm  13143
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-resscn 8794  ax-1cn 8795  ax-icn 8796  ax-addcl 8797  ax-addrcl 8798  ax-mulcl 8799  ax-mulrcl 8800  ax-addass 8802  ax-i2m1 8805  ax-1ne0 8806  ax-rrecex 8809  ax-cnre 8810
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861  df-2 9804  df-3 9805  df-4 9806  df-5 9807  df-6 9808  df-7 9809  df-8 9810  df-9 9811  df-10 9812
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