Theorem nfint 4296

Description: Bound-variable hypothesis builder for intersection. (Contributed by NM, 2-Feb-1997.) (Proof shortened by Andrew Salmon, 12-Aug-2011.)

Hypothesis

Ref	Expression
nfint.1

Assertion

Ref	Expression
nfint

Proof of Theorem nfint

Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfint2 4288	. 2
2		nfint.1	. . . 4
3		nfv 1707	. . . 4
4	2, 3	nfral 2843	. . 3
5	4	nfab 2623	. 2
6	1, 5	nfcxfr 2617	1

Syntax hints:  {cab 2442  F/_wnfc 2605  A.wral 2807  |^|cint 4286

This theorem is referenced by:  onminsb  6634  oawordeulem  7222  nnawordex  7305  rankidb  8239  cardmin2  8400  cardaleph  8491  cardmin  8960  sltval2  29416  nobndlem5  29456  aomclem8  31007

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-int 4287