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Theorem bnj1176 29448
 Description: Technical lemma for bnj69 29453. 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
bnj1176.51
bnj1176.52
Assertion
Ref Expression
bnj1176
Distinct variable groups:   ,   ,,   ,,
Allowed substitution hints:   (,)   (,)   ()   (,)

Proof of Theorem bnj1176
StepHypRef Expression
1 bnj1176.51 . . . . . . . . 9
2 bnj1176.52 . . . . . . . . 9
31, 2syl 16 . . . . . . . 8
4 df-ral 2712 . . . . . . . . 9
54rexbii 2732 . . . . . . . 8
63, 5sylib 190 . . . . . . 7
7 df-rex 2713 . . . . . . 7
86, 7sylib 190 . . . . . 6
9 19.28v 1919 . . . . . . 7
109exbii 1593 . . . . . 6
118, 10sylibr 205 . . . . 5
12 19.37v 1923 . . . . 5
1311, 12mpbir 202 . . . 4
14 19.21v 1914 . . . . 5
1514exbii 1593 . . . 4
1613, 15mpbir 202 . . 3
17 con2b 326 . . . . . . 7
1817anbi2i 677 . . . . . 6
1918imbi2i 305 . . . . 5
2019albii 1576 . . . 4
2120exbii 1593 . . 3
2216, 21mpbi 201 . 2
23 ax-1 6 . . . . 5
2423anim2i 554 . . . 4
2524imim2i 14 . . 3
2625alimi 1569 . 2
2722, 26bnj101 29162 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360  wal 1550  wex 1551   wcel 1726   wne 2601  wral 2707  wrex 2708  cvv 2958   wss 3322  c0 3630   class class class wbr 4215   wfr 4541   w-bnj17 29124 This theorem is referenced by:  bnj1190  29451 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 1667  ax-8 1688  ax-6 1745  ax-11 1762 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-ral 2712  df-rex 2713
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