Theorem nfdisj1 3995

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 3983	. 2 |- (Disj x e. A B <-> A. y E* x e. A y e. B )
2		nfrmo1 2650	. . 3 |- F/ x E* x e. A y e. B
3	2	nfal 1576	. 2 |- F/ x A. y E* x e. A y e. B
4	1, 3	nfxfr 1474	1 |- F/ xDisj x e. A B

Syntax hints:   A.wal 1351   F/wnf 1460   e. wcel 2148   E*wrmo 2458  Disj wdisj 3982

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534  ax-i5r 1535

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-eu 2029  df-mo 2030  df-rmo 2463  df-disj 3983

This theorem is referenced by: (None)