Theorem pncan3i

Description: Subtraction and addition of equals. (Contributed by NM, 26-Nov-1994)

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

Proof

Step	Hyp	Ref	Expression
1		negidi.1	⊢ 𝐴 ∈ ℂ
2		pncan3i.2	⊢ 𝐵 ∈ ℂ
3		pncan3	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( 𝐴 + ( 𝐵 − 𝐴 ) ) = 𝐵 )
4	1 2 3	mp2an	⊢ ( 𝐴 + ( 𝐵 − 𝐴 ) ) = 𝐵