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Theorem bnj1525 33560
 Description: Technical lemma for bnj1522 33563. 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
bnj1525.1
bnj1525.2
bnj1525.3
bnj1525.4
bnj1525.5
bnj1525.6
Assertion
Ref Expression
bnj1525
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,)   (,,)   (,,)   (,)   (,,)   (,,)   (,)   (,,)

Proof of Theorem bnj1525
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj1525.6 . . 3
2 bnj1525.5 . . . . 5
3 nfv 1683 . . . . . 6
4 nfv 1683 . . . . . 6
5 nfra1 2848 . . . . . 6
63, 4, 5nf3an 1877 . . . . 5
72, 6nfxfr 1625 . . . 4
8 bnj1525.4 . . . . . 6
9 bnj1525.3 . . . . . . . . 9
10 bnj1525.1 . . . . . . . . . 10
1110bnj1309 33513 . . . . . . . . 9
129, 11bnj1307 33514 . . . . . . . 8
1312nfcii 2619 . . . . . . 7
1413nfuni 4257 . . . . . 6
158, 14nfcxfr 2627 . . . . 5
16 nfcv 2629 . . . . 5
1715, 16nfne 2798 . . . 4
187, 17nfan 1875 . . 3
191, 18nfxfr 1625 . 2
2019nfri 1822 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 973  wal 1377   wceq 1379  cab 2452   wne 2662  wral 2817  wrex 2818   wss 3481  cop 4039  cuni 4251   cres 5007   wfn 5589  cfv 5594   c-bnj14 33176   w-bnj15 33180 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-uni 4252 This theorem is referenced by:  bnj1523  33562
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