Theorem nfii1 3999

Description: Bound-variable hypothesis builder for indexed intersection. (Contributed by NM, 15-Oct-2003.)

Assertion

Ref	Expression
nfii1	|- F/_x|^|_x e. A B

Proof of Theorem nfii1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-iin 3973	. 2 |- |^|_x e. A B = {y | A.x e. A y e. B}
2		nfra1 2665	. . 3 |- F/xA.x e. A y e. B
3	2	nfab 2494	. 2 |- F/_x{y | A.x e. A y e. B}
4	1, 3	nfcxfr 2487	1 |- F/_x|^|_x e. A B

Syntax hints:   e. wcel 1710  {cab 2339   F/_wnfc 2477  A.wral 2615  |^|_ciin 3971

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-ral 2620  df-iin 3973

This theorem is referenced by:  dmiin  4966