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Metamath Proof Explorer

Theorem axsep

Description: Axiom scheme of separation ax-sep derived from the axiom scheme of replacement ax-rep . The statement is identical to that of ax-sep , and therefore shows that ax-sep is redundant when ax-rep is allowed. See ax-sep for more information. (Contributed by NM, 11-Sep-2006) Use ax-sep instead. (New usage is discouraged.)

		Ref	Expression
	Assertion	axsep	⊢ ∃ 𝑦 ∀ 𝑥 ( 𝑥 ∈ 𝑦 ↔ ( 𝑥 ∈ 𝑧 ∧ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		axsepgfromrep	⊢ ∃ 𝑦 ∀ 𝑥 ( 𝑥 ∈ 𝑦 ↔ ( 𝑥 ∈ 𝑧 ∧ 𝜑 ) )