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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
StepHypRef Expression
1 sbequ12a 1994 . . . . 5
21equcoms 1795 . . . 4
32sps 1865 . . 3
43dral1 2067 . 2
5 nfnae 2058 . . 3
6 nfnae 2058 . . 3
7 nfsb2 2100 . . . 4
87naecoms 2053 . . 3
9 nfsb2 2100 . . 3
102a1i 11 . . 3
115, 6, 8, 9, 10cbv2 2020 . 2
124, 11pm2.61i 164 1
 Colors of variables: wff setvar class 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
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