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Metamath Proof Explorer

Theorem 6t6e36

Description: 6 times 6 equals 36. (Contributed by Mario Carneiro, 19-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 6t6e36 ( 6 · 6 ) = 3 6

Proof

Step Hyp Ref Expression
1 6nn0 ⊢ 6 ∈ ℕ0
2 5nn0 ⊢ 5 ∈ ℕ0
3 df-6 ⊢ 6 = ( 5 + 1 )
4 6t5e30 ⊢ ( 6 · 5 ) = 3 0
5 3nn0 ⊢ 3 ∈ ℕ0
6 5 dec0u ⊢ ( 1 0 · 3 ) = 3 0
7 4 6 eqtr4i ⊢ ( 6 · 5 ) = ( 1 0 · 3 )
8 dfdec10 ⊢ 3 6 = ( ( 1 0 · 3 ) + 6 )
9 8 eqcomi ⊢ ( ( 1 0 · 3 ) + 6 ) = 3 6
10 1 2 3 7 9 4t3lem ⊢ ( 6 · 6 ) = 3 6