Theorem 9p3e12

Description: 9 + 3 = 12. (Contributed by Mario Carneiro, 19-Apr-2015)

	Ref	Expression
Assertion	9p3e12	⊢ ( 9 + 3 ) = ; 1 2

Proof

Step	Hyp	Ref	Expression
1		9nn0	⊢ 9 ∈ ℕ0
2		2nn0	⊢ 2 ∈ ℕ0
3		1nn0	⊢ 1 ∈ ℕ0
4		df-3	⊢ 3 = ( 2 + 1 )
5		df-2	⊢ 2 = ( 1 + 1 )
6		9p2e11	⊢ ( 9 + 2 ) = ; 1 1
7	1 2 3 4 5 6	6p5lem	⊢ ( 9 + 3 ) = ; 1 2