Theorem nfdisj1 4051

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 4039	. 2 |- (Disj x e. A B <-> A. y E* x e. A y e. B )
2		nfrmo1 2684	. . 3 |- F/ x E* x e. A y e. B
3	2	nfal 1602	. 2 |- F/ x A. y E* x e. A y e. B
4	1, 3	nfxfr 1500	1 |- F/ xDisj x e. A B

Syntax hints:   A.wal 1373   F/wnf 1486   e. wcel 2180   E*wrmo 2491  Disj wdisj 4038

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 1473  ax-7 1474  ax-gen 1475  ax-ie1 1519  ax-ie2 1520  ax-4 1536  ax-ial 1560  ax-i5r 1561

This theorem depends on definitions:  df-bi 117  df-nf 1487  df-eu 2060  df-mo 2061  df-rmo 2496  df-disj 4039

This theorem is referenced by: (None)