Theorem 6p4e10OLD 11048

Description: 6 + 4 = 10. (Contributed by NM, 5-Feb-2007.) Obsolete version of 6p4e10 11474 as of 8-Sep-2021. (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
6p4e10OLD	⊢ (6 + 4) = 10

Proof of Theorem 6p4e10OLD

Step	Hyp	Ref	Expression
1		df-4 10958	. . . 4 ⊢ 4 = (3 + 1)
2	1	oveq2i 6560	. . 3 ⊢ (6 + 4) = (6 + (3 + 1))
3		6cn 10979	. . . 4 ⊢ 6 ∈ ℂ
4		3cn 10972	. . . 4 ⊢ 3 ∈ ℂ
5		ax-1cn 9873	. . . 4 ⊢ 1 ∈ ℂ
6	3, 4, 5	addassi 9927	. . 3 ⊢ ((6 + 3) + 1) = (6 + (3 + 1))
7	2, 6	eqtr4i 2635	. 2 ⊢ (6 + 4) = ((6 + 3) + 1)
8		df-10OLD 10964	. . 3 ⊢ 10 = (9 + 1)
9		6p3e9 11047	. . . 4 ⊢ (6 + 3) = 9
10	9	oveq1i 6559	. . 3 ⊢ ((6 + 3) + 1) = (9 + 1)
11	8, 10	eqtr4i 2635	. 2 ⊢ 10 = ((6 + 3) + 1)
12	7, 11	eqtr4i 2635	1 ⊢ (6 + 4) = 10

Syntax hints:   = wceq 1475  (class class class)co 6549  1c1 9816   + caddc 9818  3c3 10948  4c4 10949  6c6 10951  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:  6p4e10bOLD  11475  6p5e11OLD  11477  6t5e30OLD  11521