Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sb9i Structured version   Unicode version

Theorem sb9i 2172
 Description: Commutation of quantification and substitution variables. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sb9i

Proof of Theorem sb9i
StepHypRef Expression
1 drsb1 2114 . . . . 5
2 drsb2 2115 . . . . 5
31, 2bitr3d 248 . . . 4
43dral1 2058 . . 3
54biimprd 216 . 2
6 nfnae 2045 . . . 4
7 hbsb2 2097 . . . 4
86, 7alimd 1781 . . 3
9 stdpc4 2092 . . . . . 6
10 sbco 2160 . . . . . 6
119, 10sylib 190 . . . . 5
1211alimi 1569 . . . 4
1312a7s 1751 . . 3
148, 13syl6 32 . 2
155, 14pm2.61i 159 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1550  wsb 1659 This theorem is referenced by:  sb9  2173 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660
 Copyright terms: Public domain W3C validator