Theorem 7p5e12

Description: 7 + 5 = 12. (Contributed by Mario Carneiro, 19-Apr-2015)

	Ref	Expression
Assertion	7p5e12	⊢ ( 7 + 5 ) = ; 1 2

Proof

Step	Hyp	Ref	Expression
1		7nn0	⊢ 7 ∈ ℕ0
2		4nn0	⊢ 4 ∈ ℕ0
3		1nn0	⊢ 1 ∈ ℕ0
4		df-5	⊢ 5 = ( 4 + 1 )
5		df-2	⊢ 2 = ( 1 + 1 )
6		7p4e11	⊢ ( 7 + 4 ) = ; 1 1
7	1 2 3 4 5 6	6p5lem	⊢ ( 7 + 5 ) = ; 1 2