Theorem nfdisj1 3758

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 3746	. 2 |- (Disj x e. A B <-> A. y E* x e. A y e. B )
2		nfrmo1 2482	. . 3 |- F/ x E* x e. A y e. B
3	2	nfal 1468	. 2 |- F/ x A. y E* x e. A y e. B
4	1, 3	nfxfr 1363	1 |- F/ xDisj x e. A B

Syntax hints:   A.wal 1241   F/wnf 1349   e. wcel 1393   E*wrmo 2309  Disj wdisj 3745

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427  ax-i5r 1428

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-eu 1903  df-mo 1904  df-rmo 2314  df-disj 3746

This theorem is referenced by: (None)