Theorem sb9 2169

Description: Commutation of quantification and substitution variables. (Contributed by NM, 5-Aug-1993.) Allow a shortening of sb9i 2170. (Revised by Wolf Lammen, 15-Jun-2019.)

Assertion

Ref	Expression
sb9

Proof of Theorem sb9

Step	Hyp	Ref	Expression
1		sbequ12a 1994	. . . . 5
2	1	equcoms 1795	. . . 4
3	2	sps 1865	. . 3
4	3	dral1 2067	. 2
5		nfnae 2058	. . 3
6		nfnae 2058	. . 3
7		nfsb2 2100	. . . 4
8	7	naecoms 2053	. . 3
9		nfsb2 2100	. . 3
10	2	a1i 11	. . 3
11	5, 6, 8, 9, 10	cbv2 2020	. 2
12	4, 11	pm2.61i 164	1

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

This theorem is referenced by:  sb9i  2170

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