Theorem nfsb4t 2130

Description: A variable not free remains so after substitution with a distinct variable (closed form of nfsb4 2131). (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 4-Oct-2016.) (Proof shortened by Wolf Lammen, 11-May-2018.)

Assertion

Ref	Expression
nfsb4t

Proof of Theorem nfsb4t

Step	Hyp	Ref	Expression
1		sbequ12 1992	. . . . . . . 8
2	1	sps 1865	. . . . . . 7
3	2	drnf2 2072	. . . . . 6
4	3	biimpd 207	. . . . 5
5	4	spsd 1867	. . . 4
6	5	impcom 430	. . 3
7	6	a1d 25	. 2
8		nfnf1 1899	. . . . 5
9	8	nfal 1947	. . . 4
10		nfnae 2058	. . . 4
11	9, 10	nfan 1928	. . 3
12		nfa1 1897	. . . 4
13		nfnae 2058	. . . 4
14	12, 13	nfan 1928	. . 3
15		sp 1859	. . . 4
16	15	adantr 465	. . 3
17		nfsb2 2100	. . . 4
18	17	adantl 466	. . 3
19	1	a1i 11	. . 3
20	11, 14, 16, 18, 19	dvelimdf 2077	. 2
21	7, 20	pm2.61dan 791	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  F/wnf 1616  [wsb 1739

This theorem is referenced by:  nfsb4  2131  nfsbd  2186

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

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740