Theorem nfdisj1 3779

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 3767	. 2 |- (Disj x e. A B <-> A. y E* x e. A y e. B )
2		nfrmo1 2526	. . 3 |- F/ x E* x e. A y e. B
3	2	nfal 1508	. 2 |- F/ x A. y E* x e. A y e. B
4	1, 3	nfxfr 1403	1 |- F/ xDisj x e. A B

Syntax hints:   A.wal 1282   F/wnf 1389   e. wcel 1433   E*wrmo 2351  Disj wdisj 3766

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-ial 1467  ax-i5r 1468

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-eu 1944  df-mo 1945  df-rmo 2356  df-disj 3767

This theorem is referenced by: (None)