Metamath Proof Explorer


Theorem 9t3e27

Description: 9 times 3 equals 27. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 9t3e27 ( 9 · 3 ) = 2 7

Proof

Step Hyp Ref Expression
1 9nn0 9 ∈ ℕ0
2 2nn0 2 ∈ ℕ0
3 df-3 3 = ( 2 + 1 )
4 9t2e18 ( 9 · 2 ) = 1 8
5 1nn0 1 ∈ ℕ0
6 8nn0 8 ∈ ℕ0
7 eqid 1 8 = 1 8
8 1p1e2 ( 1 + 1 ) = 2
9 7nn0 7 ∈ ℕ0
10 1 nn0cni 9 ∈ ℂ
11 6 nn0cni 8 ∈ ℂ
12 9p8e17 ( 9 + 8 ) = 1 7
13 10 11 12 addcomli ( 8 + 9 ) = 1 7
14 5 6 1 7 8 9 13 decaddci ( 1 8 + 9 ) = 2 7
15 1 2 3 4 14 4t3lem ( 9 · 3 ) = 2 7