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Theorem 2uasbanh 28648
 Description: Distribute the unabbreviated form of proper substitution in and out of a conjunction. 2uasbanh 28648 is derived from 2uasbanhVD 29023. (Contributed by Alan Sare, 31-May-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
2uasbanh.1
Assertion
Ref Expression
2uasbanh
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)

Proof of Theorem 2uasbanh
StepHypRef Expression
1 simpl 444 . . . . 5
2 simprl 733 . . . . 5
31, 2jca 519 . . . 4
432eximi 1586 . . 3
5 simprr 734 . . . . 5
61, 5jca 519 . . . 4
762eximi 1586 . . 3
84, 7jca 519 . 2
9 2uasbanh.1 . . 3
109simplbi 447 . . . . . 6
11 simpl 444 . . . . . . . . . 10
12112eximi 1586 . . . . . . . . 9
1310, 12syl 16 . . . . . . . 8
14 a9e2ndeq 28646 . . . . . . . 8
1513, 14sylibr 204 . . . . . . 7
16 2sb5nd 28647 . . . . . . 7
1715, 16syl 16 . . . . . 6
1810, 17mpbird 224 . . . . 5
199simprbi 451 . . . . . 6
20 2sb5nd 28647 . . . . . . 7
2115, 20syl 16 . . . . . 6
2219, 21mpbird 224 . . . . 5
23 sban 2139 . . . . . . 7
2423sbbii 1665 . . . . . 6
25 sban 2139 . . . . . 6
2624, 25bitri 241 . . . . 5
2718, 22, 26sylanbrc 646 . . . 4
28 2sb5nd 28647 . . . . 5
2915, 28syl 16 . . . 4
3027, 29mpbid 202 . . 3
319, 30sylbir 205 . 2
328, 31impbii 181 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wo 358   wa 359  wal 1549  wex 1550  wsb 1658 This theorem is referenced by:  2uasban  28649 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-ne 2601  df-v 2958
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