Theorem subid1

Description: Identity law for subtraction. (Contributed by NM, 9-May-2004) (Revised by Mario Carneiro, 27-May-2016)

	Ref	Expression
Assertion	subid1	$$⊢A\in ℂ\to A-0=A$$

Proof

Step	Hyp	Ref	Expression
1		addid1	$$⊢A\in ℂ\to A+0=A$$
2	1	oveq1d	$$⊢A\in ℂ\to A+0-0=A-0$$
3		0cn	$$⊢0\in ℂ$$
4		pncan	$$⊢\left(A\in ℂ\wedge 0\in ℂ\right)\to A+0-0=A$$
5	3 4	mpan2	$$⊢A\in ℂ\to A+0-0=A$$
6	2 5	eqtr3d	$$⊢A\in ℂ\to A-0=A$$