Theorem zfausab 1704

Description: Separation Scheme in terms of a class abstraction.

Hypothesis

Ref	Expression
zfausab.1	⊢ A ∈ V

Assertion

Ref	Expression
zfausab	⊢ {x∣(x ∈ A ∧ φ)} ∈ V

Distinct variable group(s):   x,A

Proof of Theorem zfausab

Step	Hyp	Ref	Expression
1		zfausab.1	. 2 ⊢ A ∈ V
2		ssab 1555	. 2 ⊢ {x∣(x ∈ A ∧ φ)} ⊆ A
3	1, 2	ssexi 1701	1 ⊢ {x∣(x ∈ A ∧ φ)} ∈ V

Syntax hints:   ∧ wa 196  {cab 1090   ∈ wcel 1092  Vcvv 1348

This theorem is referenced by:  nnind 4434

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-14 805  ax-16 922  ax-17 925  ax-ext 1074  ax-rep 1075

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-in 1491  df-ss 1492

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