Theorem nfdisj1 3979

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 3967	. 2 |- (Disj x e. A B <-> A. y E* x e. A y e. B )
2		nfrmo1 2642	. . 3 |- F/ x E* x e. A y e. B
3	2	nfal 1569	. 2 |- F/ x A. y E* x e. A y e. B
4	1, 3	nfxfr 1467	1 |- F/ xDisj x e. A B

Syntax hints:   A.wal 1346   F/wnf 1453   e. wcel 2141   E*wrmo 2451  Disj wdisj 3966

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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527  ax-i5r 1528

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-eu 2022  df-mo 2023  df-rmo 2456  df-disj 3967

This theorem is referenced by: (None)