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Theorem bnj1133 32313
 Description: Technical lemma for bnj69 32334. 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
bnj1133.3
bnj1133.5
bnj1133.7
bnj1133.8
Assertion
Ref Expression
bnj1133
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,,)   (,,,)   (,,,)

Proof of Theorem bnj1133
StepHypRef Expression
1 bnj1133.5 . . 3
2 bnj1133.3 . . . 4
32bnj1071 32301 . . 3
41, 3bnj769 32088 . 2
5 impexp 446 . . . . . 6
65bicomi 202 . . . . 5
76albii 1611 . . . 4
8 bnj1133.8 . . . 4
97, 8mpgbir 1596 . . 3
10 df-ral 2804 . . 3
119, 10mpbir 209 . 2
12 vex 3081 . . 3
13 bnj1133.7 . . 3
1412, 13bnj110 32184 . 2
154, 11, 14sylancl 662 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1368   wceq 1370   wcel 1758  wral 2799  wsbc 3294   cdif 3434  c0 3746  csn 3986   class class class wbr 4401   cep 4739   wfr 4785   wfn 5522  com 6587   w-bnj17 32007 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4522  ax-nul 4530  ax-pr 4640  ax-un 6483 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 966  df-3an 967  df-tru 1373  df-fal 1376  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-sbc 3295  df-csb 3397  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-pss 3453  df-nul 3747  df-if 3901  df-sn 3987  df-pr 3989  df-tp 3991  df-op 3993  df-uni 4201  df-br 4402  df-opab 4460  df-tr 4495  df-eprel 4741  df-po 4750  df-so 4751  df-fr 4788  df-we 4790  df-ord 4831  df-on 4832  df-lim 4833  df-suc 4834  df-om 6588  df-bnj17 32008 This theorem is referenced by:  bnj1128  32314
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