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Theorem bnj1090 29446
 Description: Technical lemma for bnj69 29477. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1090.9
bnj1090.10
bnj1090.17
bnj1090.18
bnj1090.19
bnj1090.28
Assertion
Ref Expression
bnj1090
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,,)   (,,,)   (,,,)   (,,,)   (,,,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1090
StepHypRef Expression
1 bnj1090.28 . 2
2 impexp 435 . . . . . . 7
32exbii 1593 . . . . . 6
4 bnj1090.18 . . . . . . . . . 10
54imbi1i 317 . . . . . . . . 9
65exbii 1593 . . . . . . . 8
76imbi2i 305 . . . . . . 7
8 19.37v 1925 . . . . . . 7
9 bnj1090.10 . . . . . . . . . . . 12
109bnj115 29188 . . . . . . . . . . 11
11 bnj1090.17 . . . . . . . . . . . . 13
1211imbi2i 305 . . . . . . . . . . . 12
1312albii 1576 . . . . . . . . . . 11
1410, 13bitr4i 245 . . . . . . . . . 10
1514imbi1i 317 . . . . . . . . 9
16 19.36v 1922 . . . . . . . . 9
1715, 16bitr4i 245 . . . . . . . 8
1817imbi2i 305 . . . . . . 7
197, 8, 183bitr4i 270 . . . . . 6
203, 19bitr2i 243 . . . . 5
21 impexp 435 . . . . . 6
22 bnj256 29168 . . . . . . 7
2322imbi1i 317 . . . . . 6
24 bnj1090.9 . . . . . . 7
2524imbi2i 305 . . . . . 6
2621, 23, 253bitr4i 270 . . . . 5
2720, 26bnj133 29190 . . . 4
2827albii 1576 . . 3
29 df-ral 2716 . . 3
30 bnj1090.19 . . . . . 6
3130imbi1i 317 . . . . 5
3231exbii 1593 . . . 4
3332albii 1576 . . 3
3428, 29, 333bitr4i 270 . 2
351, 34sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551   wcel 1727  wral 2711  wsbc 3167   wss 3306   class class class wbr 4237   cep 4521   cdm 4907  cfv 5483   w-bnj17 29148 This theorem is referenced by:  bnj1030  29454 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 1668  ax-8 1689  ax-6 1746  ax-11 1763 This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-ex 1552  df-nf 1555  df-ral 2716  df-bnj17 29149
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