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Theorem bnj1374 29400
 Description: Technical lemma for bnj60 29431. 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
bnj1374.1
bnj1374.2
bnj1374.3
bnj1374.4
bnj1374.5
bnj1374.6
bnj1374.7
bnj1374.8
bnj1374.9
Assertion
Ref Expression
bnj1374
Distinct variable groups:   ,   ,   ,   ,   ,,   ,,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,,)   (,,)   (,,)   (,,,)   (,,)   (,,,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1374
StepHypRef Expression
1 bnj1374.9 . . . . . 6
21bnj1436 29211 . . . . 5
3 rexex 2765 . . . . 5
42, 3syl 16 . . . 4
5 bnj1374.1 . . . . . 6
6 bnj1374.2 . . . . . 6
7 bnj1374.3 . . . . . 6
8 bnj1374.4 . . . . . 6
9 bnj1374.8 . . . . . 6
105, 6, 7, 8, 9bnj1373 29399 . . . . 5
1110exbii 1592 . . . 4
124, 11sylib 189 . . 3
13 exsimpl 1602 . . 3
1412, 13syl 16 . 2
1514bnj937 29142 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  cab 2422   wne 2599  wral 2705  wrex 2706  crab 2709  wsbc 3161   cun 3318   wss 3320  c0 3628  csn 3814  cop 3817   class class class wbr 4212   cdm 4878   cres 4880   wfn 5449  cfv 5454   c-bnj14 29052   w-bnj15 29056   c-bnj18 29058 This theorem is referenced by:  bnj1384  29401 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-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-iun 4095  df-br 4213  df-bnj14 29053  df-bnj18 29059
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