Theorem 1p8e9 43315

Description: 1 + 8 = 9. (Contributed by SN, 24-Aug-2026.)

Assertion

Ref	Expression
1p8e9	⊢ (1 + 8) = 9

Proof of Theorem 1p8e9

Step	Hyp	Ref	Expression
1		df-8 12411	. . 3 ⊢ 8 = (7 + 1)
2	1	oveq2i 7431	. 2 ⊢ (1 + 8) = (1 + (7 + 1))
3		ax-1cn 11258	. . 3 ⊢ 1 ∈ ℂ
4		7cn 12437	. . 3 ⊢ 7 ∈ ℂ
5	3, 4, 3	addassi 11319	. 2 ⊢ ((1 + 7) + 1) = (1 + (7 + 1))
6		1p7e8 43314	. . . 4 ⊢ (1 + 7) = 8
7	6	oveq1i 7430	. . 3 ⊢ ((1 + 7) + 1) = (8 + 1)
8		8p1e9 12492	. . 3 ⊢ (8 + 1) = 9
9	7, 8	eqtri 2784	. 2 ⊢ ((1 + 7) + 1) = 9
10	2, 5, 9	3eqtr2i 2790	1 ⊢ (1 + 8) = 9

This proof depends on syntax axioms:   = wceq 1570  (class class class)co 7420  1c1 11201   + caddc 11203  7c7 12402  8c8 12403  9c9 12404

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2733  ax-1cn 11258  ax-addcl 11260  ax-addass 11265

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3414  df-v 3453  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4280  df-if 4483  df-sn 4585  df-pr 4587  df-op 4591  df-uni 4868  df-br 5104  df-iota 6494  df-fv 6546  df-ov 7423  df-2 12405  df-3 12406  df-4 12407  df-5 12408  df-6 12409  df-7 12410  df-8 12411  df-9 12412

This theorem is used by: (None)