Theorem nfii1 3882

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 3854	. 2 |- |^|_ x e. A B = { y | A. x e. A y e. B }
2		nfra1 2488	. . 3 |- F/ x A. x e. A y e. B
3	2	nfab 2304	. 2 |- F/_ x { y | A. x e. A y e. B }
4	1, 3	nfcxfr 2296	1 |- F/_ x |^|_ x e. A B

Syntax hints:   e. wcel 2128   {cab 2143   F/_wnfc 2286   A.wral 2435   |^|_ciin 3852

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-iin 3854

This theorem is referenced by:  dmiin  4834