Theorem mptresidOLD

Description: Obsolete version of mptresid as of 26-Dec-2023. (Contributed by FL, 25-Apr-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	mptresidOLD	$$⊢\left(x\in A⟼x\right)={\mathrm{I}\upharpoonright }_A$$

Proof

Step	Hyp	Ref	Expression
1		df-mpt	$$⊢\left(x\in A⟼x\right)=\left\{⟨x,y⟩|\left(x\in A\wedge y=x\right)\right\}$$
2		opabresidOLD	$$⊢\left\{⟨x,y⟩|\left(x\in A\wedge y=x\right)\right\}={\mathrm{I}\upharpoonright }_A$$
3	1 2	eqtri	$$⊢\left(x\in A⟼x\right)={\mathrm{I}\upharpoonright }_A$$