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