Theorem nfdisj1 3919

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 3907	. 2 |- (Disj x e. A B <-> A. y E* x e. A y e. B )
2		nfrmo1 2603	. . 3 |- F/ x E* x e. A y e. B
3	2	nfal 1555	. 2 |- F/ x A. y E* x e. A y e. B
4	1, 3	nfxfr 1450	1 |- F/ xDisj x e. A B

Syntax hints:   A.wal 1329   F/wnf 1436   e. wcel 1480   E*wrmo 2419  Disj wdisj 3906

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-eu 2002  df-mo 2003  df-rmo 2424  df-disj 3907

This theorem is referenced by: (None)