Theorem 8p5e13

Description: 8 + 5 = 13. (Contributed by Mario Carneiro, 19-Apr-2015)

	Ref	Expression
Assertion	8p5e13	⊢ ( 8 + 5 ) = ; 1 3

Proof

Step	Hyp	Ref	Expression
1		8nn0	⊢ 8 ∈ ℕ0
2		4nn0	⊢ 4 ∈ ℕ0
3		2nn0	⊢ 2 ∈ ℕ0
4		df-5	⊢ 5 = ( 4 + 1 )
5		df-3	⊢ 3 = ( 2 + 1 )
6		8p4e12	⊢ ( 8 + 4 ) = ; 1 2
7	1 2 3 4 5 6	6p5lem	⊢ ( 8 + 5 ) = ; 1 3