Theorem nfdisj 4434

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

Hypotheses

Ref	Expression
nfdisj.1
nfdisj.2

Assertion

Ref	Expression
nfdisj

Proof of Theorem nfdisj

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfdisj2 4424	. 2
2		nftru 1626	. . . . 5
3		nfcvf 2644	. . . . . . . 8
4		nfdisj.1	. . . . . . . . 9
5	4	a1i 11	. . . . . . . 8
6	3, 5	nfeld 2627	. . . . . . 7
7		nfdisj.2	. . . . . . . . 9
8	7	nfcri 2612	. . . . . . . 8
9	8	a1i 11	. . . . . . 7
10	6, 9	nfand 1925	. . . . . 6
11	10	adantl 466	. . . . 5
12	2, 11	nfmod2 2297	. . . 4
13	12	trud 1404	. . 3
14	13	nfal 1947	. 2
15	1, 14	nfxfr 1645	1

Syntax hints:  -.wn 3  /\wa 369  A.wal 1393  wtru 1396  F/wnf 1616  e.wcel 1818  E*wmo 2283  F/_wnfc 2605  Disj_wdisj 4422

This theorem is referenced by:  disjxiun  4449

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  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rmo 2815  df-disj 4423