Theorem elALT

Description: Alternate proof of el , shorter but requiring ax-sep . (Contributed by NM, 4-Jan-2002) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	elALT	⊢ ∃ 𝑦 𝑥 ∈ 𝑦

Proof

Step	Hyp	Ref	Expression
1		vex	⊢ 𝑥 ∈ V
2		selsALT	⊢ ( 𝑥 ∈ V → ∃ 𝑦 𝑥 ∈ 𝑦 )
3	1 2	ax-mp	⊢ ∃ 𝑦 𝑥 ∈ 𝑦