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Theorem 6p4e10OLD 11131
Description: 6 + 4 = 10. (Contributed by NM, 5-Feb-2007.) Obsolete version of 6p4e10 11558 as of 8-Sep-2021. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
6p4e10OLD (6 + 4) = 10

Proof of Theorem 6p4e10OLD
StepHypRef Expression
1 df-4 11041 . . . 4 4 = (3 + 1)
21oveq2i 6626 . . 3 (6 + 4) = (6 + (3 + 1))
3 6cn 11062 . . . 4 6 ∈ ℂ
4 3cn 11055 . . . 4 3 ∈ ℂ
5 ax-1cn 9954 . . . 4 1 ∈ ℂ
63, 4, 5addassi 10008 . . 3 ((6 + 3) + 1) = (6 + (3 + 1))
72, 6eqtr4i 2646 . 2 (6 + 4) = ((6 + 3) + 1)
8 df-10OLD 11047 . . 3 10 = (9 + 1)
9 6p3e9 11130 . . . 4 (6 + 3) = 9
109oveq1i 6625 . . 3 ((6 + 3) + 1) = (9 + 1)
118, 10eqtr4i 2646 . 2 10 = ((6 + 3) + 1)
127, 11eqtr4i 2646 1 (6 + 4) = 10
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  (class class class)co 6615  1c1 9897   + caddc 9899  3c3 11031  4c4 11032  6c6 11034  9c9 11037  10c10 11038
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 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-resscn 9953  ax-1cn 9954  ax-icn 9955  ax-addcl 9956  ax-addrcl 9957  ax-mulcl 9958  ax-mulrcl 9959  ax-addass 9961  ax-i2m1 9964  ax-1ne0 9965  ax-rrecex 9968  ax-cnre 9969
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 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ne 2791  df-ral 2913  df-rex 2914  df-rab 2917  df-v 3192  df-dif 3563  df-un 3565  df-in 3567  df-ss 3574  df-nul 3898  df-if 4065  df-sn 4156  df-pr 4158  df-op 4162  df-uni 4410  df-br 4624  df-iota 5820  df-fv 5865  df-ov 6618  df-2 11039  df-3 11040  df-4 11041  df-5 11042  df-6 11043  df-7 11044  df-8 11045  df-9 11046  df-10OLD 11047
This theorem is referenced by:  6p4e10bOLD  11559  6p5e11OLD  11561  6t5e30OLD  11605
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