Theorem subnegi

Description: Relationship between subtraction and negative. (Contributed by NM, 1-Dec-2005)

	Ref	Expression
Hypotheses	negidi.1	⊢ 𝐴 ∈ ℂ
	pncan3i.2	⊢ 𝐵 ∈ ℂ
Assertion	subnegi	⊢ ( 𝐴 − - 𝐵 ) = ( 𝐴 + 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		negidi.1	⊢ 𝐴 ∈ ℂ
2		pncan3i.2	⊢ 𝐵 ∈ ℂ
3		subneg	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( 𝐴 − - 𝐵 ) = ( 𝐴 + 𝐵 ) )
4	1 2 3	mp2an	⊢ ( 𝐴 − - 𝐵 ) = ( 𝐴 + 𝐵 )