Theorem nfdisj1 4435

Description: Bound-variable hypothesis builder for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)

Assertion

Ref	Expression
nfdisj1

Proof of Theorem nfdisj1

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-disj 4423	. 2
2		nfrmo1 3029	. . 3
3	2	nfal 1947	. 2
4	1, 3	nfxfr 1645	1

Syntax hints:  A.wal 1393  F/wnf 1616  e.wcel 1818  E*wrmo 2810  Disj_wdisj 4422

This theorem is referenced by:  disjabrex  27443  disjabrexf  27444  hasheuni  28091  measvunilem  28183  measvunilem0  28184  measvuni  28185  measinblem  28191  voliune  28201  volfiniune  28202  volmeas  28203  dstrvprob  28410

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287  df-rmo 2815  df-disj 4423