Theorem cnm2m1cnm3

Description: Subtracting 2 and afterwards 1 from a number results in the difference between the number and 3. (Contributed by Alexander van der Vekens, 16-Sep-2018)

	Ref	Expression
Assertion	cnm2m1cnm3	$$⊢A\in ℂ\to A-2-1=A-3$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢A\in ℂ\to A\in ℂ$$
2		2cnd	$$⊢A\in ℂ\to 2\in ℂ$$
3		1cnd	$$⊢A\in ℂ\to 1\in ℂ$$
4	1 2 3	subsub4d	$$⊢A\in ℂ\to A-2-1=A-\left(2+1\right)$$
5		2p1e3	$$⊢2+1=3$$
6	5	a1i	$$⊢A\in ℂ\to 2+1=3$$
7	6	oveq2d	$$⊢A\in ℂ\to A-\left(2+1\right)=A-3$$
8	4 7	eqtrd	$$⊢A\in ℂ\to A-2-1=A-3$$