Theorem hbii1 2575

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 2559	. 2 |- |^|_x e. A B = {z | A.x e. A z e. B}
2		hbra1 1679	. . 3 |- (A.x e. A z e. B -> A.xA.x e. A z e. B)
3	2	hbab 1460	. 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 1555	1 |- (y e. |^|_x e. A B -> A.x y e. |^|_x e. A B)

Syntax hints:   -> wi 3  A.wal 951   e. wcel 955  {cab 1456  A.wral 1637  |^|_ciin 2557

This theorem is referenced by:  scott0 4689

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-ral 1641  df-iin 2559

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