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Theorem 5p5e10OLD 11045
Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007.) Obsolete version of 5p5e10 11472 as of 8-Sep-2021. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
5p5e10OLD (5 + 5) = 10

Proof of Theorem 5p5e10OLD
StepHypRef Expression
1 df-5 10959 . . . 4 5 = (4 + 1)
21oveq2i 6560 . . 3 (5 + 5) = (5 + (4 + 1))
3 5cn 10977 . . . 4 5 ∈ ℂ
4 4cn 10975 . . . 4 4 ∈ ℂ
5 ax-1cn 9873 . . . 4 1 ∈ ℂ
63, 4, 5addassi 9927 . . 3 ((5 + 4) + 1) = (5 + (4 + 1))
72, 6eqtr4i 2635 . 2 (5 + 5) = ((5 + 4) + 1)
8 df-10OLD 10964 . . 3 10 = (9 + 1)
9 5p4e9 11044 . . . 4 (5 + 4) = 9
109oveq1i 6559 . . 3 ((5 + 4) + 1) = (9 + 1)
118, 10eqtr4i 2635 . 2 10 = ((5 + 4) + 1)
127, 11eqtr4i 2635 1 (5 + 5) = 10
Colors of variables: wff setvar class
Syntax hints:   = wceq 1475  (class class class)co 6549  1c1 9816   + caddc 9818  4c4 10949  5c5 10950  9c9 10954  10c10 10955
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-resscn 9872  ax-1cn 9873  ax-icn 9874  ax-addcl 9875  ax-addrcl 9876  ax-mulcl 9877  ax-mulrcl 9878  ax-addass 9880  ax-i2m1 9883  ax-1ne0 9884  ax-rrecex 9887  ax-cnre 9888
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ne 2782  df-ral 2901  df-rex 2902  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-uni 4373  df-br 4584  df-iota 5768  df-fv 5812  df-ov 6552  df-2 10956  df-3 10957  df-4 10958  df-5 10959  df-6 10960  df-7 10961  df-8 10962  df-9 10963  df-10OLD 10964
This theorem is referenced by:  5t2e10OLD  11059  5p5e10bOLD  11473  5t4e20OLD  11514
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