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Theorem 2sb5nd 28326
 Description: Equivalence for double substitution 2sb5 2051 without distinct , requirement. 2sb5nd 28326 is derived from 2sb5ndVD 28686. (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 28325 . 2
2 anabs5 784 . . . 4
3 2pm13.193 28318 . . . . . . . . 9
43exbii 1569 . . . . . . . 8
5 nfs1v 2045 . . . . . . . . . 10
65nfsb 2048 . . . . . . . . 9
7619.41 1815 . . . . . . . 8
84, 7bitr3i 242 . . . . . . 7
98exbii 1569 . . . . . 6
10 nfs1v 2045 . . . . . . 7
111019.41 1815 . . . . . 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 1527  wex 1528   wceq 1623  wsb 1629 This theorem is referenced by:  2uasbanh  28327  2uasbanhVD  28687 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-fal 1311  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-ne 2448  df-v 2790
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