Theorem nfdisj1 4036

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 4024	. 2 |- (Disj x e. A B <-> A. y E* x e. A y e. B )
2		nfrmo1 2680	. . 3 |- F/ x E* x e. A y e. B
3	2	nfal 1600	. 2 |- F/ x A. y E* x e. A y e. B
4	1, 3	nfxfr 1498	1 |- F/ xDisj x e. A B

Syntax hints:   A.wal 1371   F/wnf 1484   e. wcel 2177   E*wrmo 2488  Disj wdisj 4023

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-ial 1558  ax-i5r 1559

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-eu 2058  df-mo 2059  df-rmo 2493  df-disj 4024

This theorem is referenced by: (None)