Theorem bj-elissetALT

Description: Alternate proof of elisset . This is essentially the same proof as seen by inlining bj-denotes and bj-denoteslem . Use elissetv instead when sufficient (in particular when V is substituted for _V ). (Contributed by BJ, 29-Apr-2019) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	bj-elissetALT	⊢ ( 𝐴 ∈ 𝑉 → ∃ 𝑥 𝑥 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		elissetv	⊢ ( 𝐴 ∈ 𝑉 → ∃ 𝑦 𝑦 = 𝐴 )
2		bj-denotes	⊢ ( ∃ 𝑦 𝑦 = 𝐴 ↔ ∃ 𝑥 𝑥 = 𝐴 )
3	1 2	sylib	⊢ ( 𝐴 ∈ 𝑉 → ∃ 𝑥 𝑥 = 𝐴 )