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Metamath Proof Explorer

Theorem 5t5e25

Description: 5 times 5 equals 25. (Contributed by Mario Carneiro, 19-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 5t5e25 ( 5 · 5 ) = 2 5

Proof

Step Hyp Ref Expression
1 5nn0 ⊢ 5 ∈ ℕ0
2 4nn0 ⊢ 4 ∈ ℕ0
3 df-5 ⊢ 5 = ( 4 + 1 )
4 5t4e20 ⊢ ( 5 · 4 ) = 2 0
5 2nn0 ⊢ 2 ∈ ℕ0
6 5 dec0u ⊢ ( 1 0 · 2 ) = 2 0
7 4 6 eqtr4i ⊢ ( 5 · 4 ) = ( 1 0 · 2 )
8 dfdec10 ⊢ 2 5 = ( ( 1 0 · 2 ) + 5 )
9 8 eqcomi ⊢ ( ( 1 0 · 2 ) + 5 ) = 2 5
10 1 2 3 7 9 4t3lem ⊢ ( 5 · 5 ) = 2 5