Theorem issetri 1353

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(s):   x,A

Proof of Theorem issetri

Step	Hyp	Ref	Expression
1		issetri.1	. 2 |- E.x x = A
2		isset 1351	. 2 |- (A e. V <-> E.x x = A)
3	1, 2	mpbir 165	1 |- A e. V

Syntax hints:  E.wex 678   = wceq 1091   e. wcel 1092  Vcvv 1348

This theorem is referenced by:  zfrep4 1479  inex1 1697  pwex 1806  uniex 1947

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-gen 677  ax-9 799  ax-12 802  ax-17 925  ax-ext 1074

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

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