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Theorem bnj1445 29925
 Description: Technical lemma for bnj60 29943. 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
bnj1445.1
bnj1445.2
bnj1445.3
bnj1445.4
bnj1445.5
bnj1445.6
bnj1445.7
bnj1445.8
bnj1445.9
bnj1445.10
bnj1445.11
bnj1445.12
bnj1445.13
bnj1445.14
bnj1445.15
bnj1445.16
bnj1445.17
bnj1445.18
bnj1445.19
bnj1445.20
bnj1445.21
bnj1445.22
bnj1445.23
Assertion
Ref Expression
bnj1445
Distinct variable groups:   ,,   ,   ,   ,,   ,,   ,,   ,
Allowed substitution hints:   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,)   (,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,)   (,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)

Proof of Theorem bnj1445
StepHypRef Expression
1 bnj1445.21 . 2
2 bnj1445.20 . . . . 5
3 bnj1445.19 . . . . . . 7
4 bnj1445.17 . . . . . . . . 9
5 bnj1445.7 . . . . . . . . . . . . 13
6 bnj1445.6 . . . . . . . . . . . . . . 15
7 nfv 1769 . . . . . . . . . . . . . . . 16
8 bnj1445.5 . . . . . . . . . . . . . . . . . 18
9 bnj1445.4 . . . . . . . . . . . . . . . . . . . . . 22
10 bnj1445.3 . . . . . . . . . . . . . . . . . . . . . . . . 25
11 nfre1 2846 . . . . . . . . . . . . . . . . . . . . . . . . . 26
1211nfab 2616 . . . . . . . . . . . . . . . . . . . . . . . . 25
1310, 12nfcxfr 2610 . . . . . . . . . . . . . . . . . . . . . . . 24
1413nfcri 2606 . . . . . . . . . . . . . . . . . . . . . . 23
15 nfv 1769 . . . . . . . . . . . . . . . . . . . . . . 23
1614, 15nfan 2031 . . . . . . . . . . . . . . . . . . . . . 22
179, 16nfxfr 1704 . . . . . . . . . . . . . . . . . . . . 21
1817nfex 2050 . . . . . . . . . . . . . . . . . . . 20
1918nfn 2003 . . . . . . . . . . . . . . . . . . 19
20 nfcv 2612 . . . . . . . . . . . . . . . . . . 19
2119, 20nfrab 2958 . . . . . . . . . . . . . . . . . 18
228, 21nfcxfr 2610 . . . . . . . . . . . . . . . . 17
23 nfcv 2612 . . . . . . . . . . . . . . . . 17
2422, 23nfne 2742 . . . . . . . . . . . . . . . 16
257, 24nfan 2031 . . . . . . . . . . . . . . 15
266, 25nfxfr 1704 . . . . . . . . . . . . . 14
2722nfcri 2606 . . . . . . . . . . . . . 14
28 nfv 1769 . . . . . . . . . . . . . . 15
2922, 28nfral 2789 . . . . . . . . . . . . . 14
3026, 27, 29nf3an 2033 . . . . . . . . . . . . 13
315, 30nfxfr 1704 . . . . . . . . . . . 12
3231nfri 1972 . . . . . . . . . . 11
3332bnj1351 29710 . . . . . . . . . 10
3433nfi 1682 . . . . . . . . 9
354, 34nfxfr 1704 . . . . . . . 8
36 nfv 1769 . . . . . . . 8
3735, 36nfan 2031 . . . . . . 7
383, 37nfxfr 1704 . . . . . 6
39 bnj1445.9 . . . . . . . 8
40 nfcv 2612 . . . . . . . . . 10
41 bnj1445.8 . . . . . . . . . . 11
42 nfcv 2612 . . . . . . . . . . . 12
4342, 17nfsbc 3277 . . . . . . . . . . 11
4441, 43nfxfr 1704 . . . . . . . . . 10
4540, 44nfrex 2848 . . . . . . . . 9
4645nfab 2616 . . . . . . . 8
4739, 46nfcxfr 2610 . . . . . . 7
4847nfcri 2606 . . . . . 6
49 nfv 1769 . . . . . 6
5038, 48, 49nf3an 2033 . . . . 5
512, 50nfxfr 1704 . . . 4
5251nfri 1972 . . 3
53 ax-5 1766 . . 3
5414nfri 1972 . . 3
55 ax-5 1766 . . 3
5652, 53, 54, 55bnj982 29662 . 2
571, 56hbxfrbi 1702 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 189   wa 376   w3a 1007  wal 1450   wceq 1452  wex 1671   wcel 1904  cab 2457   wne 2641  wral 2756  wrex 2757  crab 2760  wsbc 3255   cun 3388   wss 3390  c0 3722  csn 3959  cop 3965  cuni 4190   class class class wbr 4395   cdm 4839   cres 4841   wfn 5584  cfv 5589   w-bnj17 29563   c-bnj14 29565   w-bnj15 29569   c-bnj18 29571 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-sbc 3256  df-bnj17 29564 This theorem is referenced by:  bnj1450  29931
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