Theorem dfin5 2052

Description: Alternate definition for the intersection of two classes.

Assertion

Ref	Expression
dfin5	|- (A i^i B) = {x e. A | x e. B}

Distinct variable groups:   x,A   x,B

Proof of Theorem dfin5

Step	Hyp	Ref	Expression
1		df-in 2051	. 2 |- (A i^i B) = {x | (x e. A /\ x e. B)}
2		df-rab 1652	. 2 |- {x e. A | x e. B} = {x | (x e. A /\ x e. B)}
3	1, 2	eqtr4 1498	1 |- (A i^i B) = {x e. A | x e. B}

Syntax hints:   /\ wa 223   = wceq 956   e. wcel 958  {cab 1463  {crab 1648   i^i cin 2046

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

This theorem depends on definitions:  df-bi 147  df-an 225  df-cleq 1469  df-rab 1652  df-in 2051

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