Metamath Proof Explorer

Theorem 8t6e48

Description: 8 times 6 equals 48. (Contributed by Mario Carneiro, 19-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 8t6e48 ( 8 · 6 ) = 4 8

Proof

Step Hyp Ref Expression
1 8nn0 ⊢ 8 ∈ ℕ0
2 5nn0 ⊢ 5 ∈ ℕ0
3 df-6 ⊢ 6 = ( 5 + 1 )
4 8t5e40 ⊢ ( 8 · 5 ) = 4 0
5 4nn0 ⊢ 4 ∈ ℕ0
6 5 dec0u ⊢ ( 1 0 · 4 ) = 4 0
7 4 6 eqtr4i ⊢ ( 8 · 5 ) = ( 1 0 · 4 )
8 dfdec10 ⊢ 4 8 = ( ( 1 0 · 4 ) + 8 )
9 8 eqcomi ⊢ ( ( 1 0 · 4 ) + 8 ) = 4 8
10 1 2 3 7 9 4t3lem ⊢ ( 8 · 6 ) = 4 8