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Theorem 5p5e10 8698
Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.)
Assertion
Ref Expression
5p5e10 (5 + 5) = 10

Proof of Theorem 5p5e10
StepHypRef Expression
1 df-5 8238 . . . 4 5 = (4 + 1)
21oveq2i 5575 . . 3 (5 + 5) = (5 + (4 + 1))
3 5cn 8256 . . . 4 5 ∈ ℂ
4 4cn 8254 . . . 4 4 ∈ ℂ
5 ax-1cn 7201 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7259 . . 3 ((5 + 4) + 1) = (5 + (4 + 1))
72, 6eqtr4i 2106 . 2 (5 + 5) = ((5 + 4) + 1)
8 5p4e9 8317 . . 3 (5 + 4) = 9
98oveq1i 5574 . 2 ((5 + 4) + 1) = (9 + 1)
10 9p1e10 8630 . 2 (9 + 1) = 10
117, 9, 103eqtri 2107 1 (5 + 5) = 10
Colors of variables: wff set class
Syntax hints:   = wceq 1285  (class class class)co 5564  0cc0 7113  1c1 7114   + caddc 7116  4c4 8228  5c5 8229  9c9 8233  cdc 8628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3916  ax-cnex 7199  ax-resscn 7200  ax-1cn 7201  ax-1re 7202  ax-icn 7203  ax-addcl 7204  ax-addrcl 7205  ax-mulcl 7206  ax-mulcom 7209  ax-addass 7210  ax-mulass 7211  ax-distr 7212  ax-1rid 7215  ax-0id 7216  ax-cnre 7219
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-rab 2362  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-sn 3422  df-pr 3423  df-op 3425  df-uni 3622  df-int 3657  df-br 3806  df-iota 4917  df-fv 4960  df-ov 5567  df-inn 8177  df-2 8235  df-3 8236  df-4 8237  df-5 8238  df-6 8239  df-7 8240  df-8 8241  df-9 8242  df-dec 8629
This theorem is referenced by:  5t2e10  8727  5t4e20  8729
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