Theorem issetri 1807

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 1805	. 2 |- (A e. V <-> E.x x = A)
3	1, 2	mpbir 190	1 |- A e. V

Syntax hints:   = wceq 953   e. wcel 955  E.wex 977  Vcvv 1802

This theorem is referenced by:  zfrep4 2691  inex1 2706  pwex 2735  zfpair2 2770  uniex 2861

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803

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