Theorem intiin 2602

Description: Class intersection in terms of indexed intersection. Definition of [Stoll] p. 44.

Assertion

Ref	Expression
intiin	|- |^|A = |^|_x e. A x

Distinct variable group:   x,A

Proof of Theorem intiin

Step	Hyp	Ref	Expression
1		dfint2 2535	. 2 |- |^|A = {y | A.x e. A y e. x}
2		df-iin 2569	. 2 |- |^|_x e. A x = {y | A.x e. A y e. x}
3	1, 2	eqtr4 1498	1 |- |^|A = |^|_x e. A x

Syntax hints:   = wceq 956   e. wcel 958  {cab 1463  A.wral 1645  |^|cint 2533  |^|_ciin 2567

This theorem is referenced by:  intcld 7680

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  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-ral 1649  df-int 2534  df-iin 2569

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