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Theorem 2sb5nd 28548
 Description: Equivalence for double substitution 2sb5 2187 without distinct , requirement. 2sb5nd 28548 is derived from 2sb5ndVD 28923. (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 28547 . 2
2 anabs5 785 . . . 4
3 2pm13.193 28540 . . . . . . . . 9
43exbii 1592 . . . . . . . 8
5 nfs1v 2181 . . . . . . . . . 10
65nfsb 2184 . . . . . . . . 9
7619.41 1900 . . . . . . . 8
84, 7bitr3i 243 . . . . . . 7
98exbii 1592 . . . . . 6
10 nfs1v 2181 . . . . . . 7
111019.41 1900 . . . . . 6
129, 11bitr2i 242 . . . . 5
1312anbi2i 676 . . . 4
142, 13bitr3i 243 . . 3
15 pm5.32 618 . . 3
1614, 15mpbir 201 . 2
171, 16sylbi 188 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359  wal 1549  wex 1550   wceq 1652  wsb 1658 This theorem is referenced by:  2uasbanh  28549  2uasbanhVD  28924 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-ne 2600  df-v 2950
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