Mathbox for Alan Sare < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  2sb5nd Unicode version

Theorem 2sb5nd 28625
 Description: Equivalence for double substitution 2sb5 2064 without distinct , requirement. 2sb5nd 28625 is derived from 2sb5ndVD 29002. (Contributed by Alan Sare, 30-Apr-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
2sb5nd
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem 2sb5nd
StepHypRef Expression
1 a9e2ndeq 28624 . 2
2 anabs5 784 . . . 4
3 2pm13.193 28617 . . . . . . . . 9
43exbii 1572 . . . . . . . 8
5 nfs1v 2058 . . . . . . . . . 10
65nfsb 2061 . . . . . . . . 9
7619.41 1827 . . . . . . . 8
84, 7bitr3i 242 . . . . . . 7
98exbii 1572 . . . . . 6
10 nfs1v 2058 . . . . . . 7
111019.41 1827 . . . . . 6
129, 11bitr2i 241 . . . . 5
1312anbi2i 675 . . . 4
142, 13bitr3i 242 . . 3
15 pm5.32 617 . . 3
1614, 15mpbir 200 . 2
171, 16sylbi 187 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wo 357   wa 358  wal 1530  wex 1531   wceq 1632  wsb 1638 This theorem is referenced by:  2uasbanh  28626  2uasbanhVD  29003 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-ne 2461  df-v 2803
 Copyright terms: Public domain W3C validator