Theorem nfdisj1 4008

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 3996	. 2 |- (Disj x e. A B <-> A. y E* x e. A y e. B )
2		nfrmo1 2663	. . 3 |- F/ x E* x e. A y e. B
3	2	nfal 1587	. 2 |- F/ x A. y E* x e. A y e. B
4	1, 3	nfxfr 1485	1 |- F/ xDisj x e. A B

Syntax hints:   A.wal 1362   F/wnf 1471   e. wcel 2160   E*wrmo 2471  Disj wdisj 3995

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-eu 2041  df-mo 2042  df-rmo 2476  df-disj 3996

This theorem is referenced by: (None)