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Theorem bnj1176 29807
 Description: Technical lemma for bnj69 29812. 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 17 . . . . . . . 8
4 df-ral 2741 . . . . . . . . 9
54rexbii 2888 . . . . . . . 8
63, 5sylib 200 . . . . . . 7
7 df-rex 2742 . . . . . . 7
86, 7sylib 200 . . . . . 6
9 19.28v 1824 . . . . . . 7
109exbii 1717 . . . . . 6
118, 10sylibr 216 . . . . 5
12 19.37v 1825 . . . . 5
1311, 12mpbir 213 . . . 4
14 19.21v 1785 . . . . 5
1514exbii 1717 . . . 4
1613, 15mpbir 213 . . 3
17 con2b 336 . . . . . . 7
1817anbi2i 699 . . . . . 6
1918imbi2i 314 . . . . 5
2019albii 1690 . . . 4
2120exbii 1717 . . 3
2216, 21mpbi 212 . 2
23 ax-1 6 . . . . 5
2423anim2i 572 . . . 4
2524imim2i 16 . . 3
2625alimi 1683 . 2
2722, 26bnj101 29522 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 371  wal 1441  wex 1662   wcel 1886   wne 2621  wral 2736  wrex 2737  cvv 3044   wss 3403  c0 3730   class class class wbr 4401   wfr 4789   w-bnj17 29484 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-ral 2741  df-rex 2742 This theorem is referenced by:  bnj1190  29810
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