Theorem issetri 1813

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 1811	. 2 |- (A e. V <-> E.x x = A)
3	1, 2	mpbir 190	1 |- A e. V

Syntax hints:   = wceq 955   e. wcel 957  E.wex 979  Vcvv 1808

This theorem is referenced by:  zfrep4 2697  inex1 2712  pwex 2741  zfpair2 2776  uniex 2866

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 962  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-ext 1458

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1171  df-clab 1463  df-cleq 1468  df-clel 1471  df-v 1809

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