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	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝑥 ) = ( I ↾ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		df-mpt	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝑥 ) = { ⟨ 𝑥 , 𝑦 ⟩ ∣ ( 𝑥 ∈ 𝐴 ∧ 𝑦 = 𝑥 ) }
2		opabresidOLD	⊢ { ⟨ 𝑥 , 𝑦 ⟩ ∣ ( 𝑥 ∈ 𝐴 ∧ 𝑦 = 𝑥 ) } = ( I ↾ 𝐴 )
3	1 2	eqtri	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝑥 ) = ( I ↾ 𝐴 )