Theorem hbii1 2589

Description: Bound-variable hypothesis builder for indexed intersection.

Assertion

Ref	Expression
hbii1	|- (y e. |^|_x e. A B -> A.x y e. |^|_x e. A B)

Distinct variable group:   x,y

Proof of Theorem hbii1

Step	Hyp	Ref	Expression
1		df-iin 2573	. 2 |- |^|_x e. A B = {z | A.x e. A z e. B}
2		hbra1 1690	. . 3 |- (A.x e. A z e. B -> A.xA.x e. A z e. B)
3	2	hbab 1470	. 2 |- (y e. {z | A.x e. A z e. B} -> A.x y e. {z | A.x e. A z e. B})
4	1, 3	hbxfr 1566	1 |- (y e. |^|_x e. A B -> A.x y e. |^|_x e. A B)

Syntax hints:   -> wi 3  A.wal 956   e. wcel 960  {cab 1466  A.wral 1648  |^|_ciin 2571

This theorem is referenced by:  scott0 4727

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-ral 1652  df-iin 2573

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