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Metamath Proof Explorer

Theorem 9p3e12

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

		Ref	Expression
	Assertion	9p3e12	$⊢ 9 + 3 = 12$

Step	Hyp	Ref	Expression
1		9nn0	$⊢ 9 \in ℕ_{0}$
2		2nn0	$⊢ 2 \in ℕ_{0}$
3		1nn0	$⊢ 1 \in ℕ_{0}$
4		df-3	$⊢ 3 = 2 + 1$
5		df-2	$⊢ 2 = 1 + 1$
6		9p2e11	$⊢ 9 + 2 = 11$
7	1 2 3 4 5 6	6p5lem	$⊢ 9 + 3 = 12$