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Theorem 7p3e10OLD 11118
Description: 7 + 3 = 10. (Contributed by NM, 5-Feb-2007.) Obsolete version of 7p3e10 11547 as of 8-Sep-2021. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
7p3e10OLD (7 + 3) = 10

Proof of Theorem 7p3e10OLD
StepHypRef Expression
1 df-3 11025 . . . 4 3 = (2 + 1)
21oveq2i 6616 . . 3 (7 + 3) = (7 + (2 + 1))
3 7cn 11049 . . . 4 7 ∈ ℂ
4 2cn 11036 . . . 4 2 ∈ ℂ
5 ax-1cn 9939 . . . 4 1 ∈ ℂ
63, 4, 5addassi 9993 . . 3 ((7 + 2) + 1) = (7 + (2 + 1))
72, 6eqtr4i 2651 . 2 (7 + 3) = ((7 + 2) + 1)
8 df-10OLD 11032 . . 3 10 = (9 + 1)
9 7p2e9 11117 . . . 4 (7 + 2) = 9
109oveq1i 6615 . . 3 ((7 + 2) + 1) = (9 + 1)
118, 10eqtr4i 2651 . 2 10 = ((7 + 2) + 1)
127, 11eqtr4i 2651 1 (7 + 3) = 10
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  (class class class)co 6605  1c1 9882   + caddc 9884  2c2 11015  3c3 11016  7c7 11020  9c9 11022  10c10 11023
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-9 2001  ax-10 2021  ax-11 2036  ax-12 2049  ax-13 2250  ax-ext 2606  ax-resscn 9938  ax-1cn 9939  ax-icn 9940  ax-addcl 9941  ax-addrcl 9942  ax-mulcl 9943  ax-mulrcl 9944  ax-addass 9946  ax-i2m1 9949  ax-1ne0 9950  ax-rrecex 9953  ax-cnre 9954
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1883  df-clab 2613  df-cleq 2619  df-clel 2622  df-nfc 2756  df-ne 2797  df-ral 2917  df-rex 2918  df-rab 2921  df-v 3193  df-dif 3563  df-un 3565  df-in 3567  df-ss 3574  df-nul 3897  df-if 4064  df-sn 4154  df-pr 4156  df-op 4160  df-uni 4408  df-br 4619  df-iota 5813  df-fv 5858  df-ov 6608  df-2 11024  df-3 11025  df-4 11026  df-5 11027  df-6 11028  df-7 11029  df-8 11030  df-9 11031  df-10OLD 11032
This theorem is referenced by:  7p3e10bOLD  11548  7p4e11OLD  11550
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