Theorem nfdisj1 4097

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 4085	. 2 |- (Disj x e. A B <-> A. y E* x e. A y e. B )
2		nfrmo1 2716	. . 3 |- F/ x E* x e. A y e. B
3	2	nfal 1625	. 2 |- F/ x A. y E* x e. A y e. B
4	1, 3	nfxfr 1523	1 |- F/ xDisj x e. A B

Syntax hints:   A.wal 1396   F/wnf 1509   e. wcel 2203   E*wrmo 2523  Disj wdisj 4084

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-ial 1583  ax-i5r 1584

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-eu 2083  df-mo 2084  df-rmo 2528  df-disj 4085

This theorem is referenced by: (None)