Theorem nfdisj1 3927

Description: Bound-variable hypothesis builder for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)

Assertion

Ref	Expression
nfdisj1	|- F/ xDisj x e. A B

Proof of Theorem nfdisj1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-disj 3915	. 2 |- (Disj x e. A B <-> A. y E* x e. A y e. B )
2		nfrmo1 2606	. . 3 |- F/ x E* x e. A y e. B
3	2	nfal 1556	. 2 |- F/ x A. y E* x e. A y e. B
4	1, 3	nfxfr 1451	1 |- F/ xDisj x e. A B

Syntax hints:   A.wal 1330   F/wnf 1437   e. wcel 1481   E*wrmo 2420  Disj wdisj 3914

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-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-ial 1515  ax-i5r 1516

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-eu 2003  df-mo 2004  df-rmo 2425  df-disj 3915

This theorem is referenced by: (None)