Theorem issetri 1816

Description: A way to say "A is a set" (inference rule).

Hypothesis

Ref	Expression
issetri.1	|- E.x x = A

Assertion

Ref	Expression
issetri	|- A e. V

Distinct variable group:   x,A

Proof of Theorem issetri

Step	Hyp	Ref	Expression
1		issetri.1	. 2 |- E.x x = A
2		isset 1814	. 2 |- (A e. V <-> E.x x = A)
3	1, 2	mpbir 190	1 |- A e. V

Syntax hints:   = wceq 956   e. wcel 958  E.wex 980  Vcvv 1811

This theorem is referenced by:  zfrep4 2701  inex1 2716  pwex 2745  zfpair2 2780  uniex 2870

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812

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