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Theorem bnj1446 29642
 Description: Technical lemma for bnj60 29659. 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
bnj1446.1
bnj1446.2
bnj1446.3
bnj1446.4
bnj1446.5
bnj1446.6
bnj1446.7
bnj1446.8
bnj1446.9
bnj1446.10
bnj1446.11
bnj1446.12
bnj1446.13
Assertion
Ref Expression
bnj1446
Distinct variable groups:   ,,   ,   ,   ,,   ,,   ,,   ,
Allowed substitution hints:   (,,,,)   (,,,,)   (,,,,)   (,,)   (,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,)   (,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)

Proof of Theorem bnj1446
StepHypRef Expression
1 bnj1446.12 . . . . 5
2 bnj1446.10 . . . . . . 7
3 bnj1446.9 . . . . . . . . 9
4 nfcv 2591 . . . . . . . . . . 11
5 bnj1446.8 . . . . . . . . . . . 12
6 nfcv 2591 . . . . . . . . . . . . 13
7 bnj1446.4 . . . . . . . . . . . . . 14
8 bnj1446.3 . . . . . . . . . . . . . . . . 17
9 nfre1 2893 . . . . . . . . . . . . . . . . . 18
109nfab 2595 . . . . . . . . . . . . . . . . 17
118, 10nfcxfr 2589 . . . . . . . . . . . . . . . 16
1211nfcri 2584 . . . . . . . . . . . . . . 15
13 nfv 1754 . . . . . . . . . . . . . . 15
1412, 13nfan 1986 . . . . . . . . . . . . . 14
157, 14nfxfr 1692 . . . . . . . . . . . . 13
166, 15nfsbc 3327 . . . . . . . . . . . 12
175, 16nfxfr 1692 . . . . . . . . . . 11
184, 17nfrex 2895 . . . . . . . . . 10
1918nfab 2595 . . . . . . . . 9
203, 19nfcxfr 2589 . . . . . . . 8
2120nfuni 4228 . . . . . . 7
222, 21nfcxfr 2589 . . . . . 6
23 nfcv 2591 . . . . . . . 8
24 nfcv 2591 . . . . . . . . 9
25 bnj1446.11 . . . . . . . . . 10
2622, 4nfres 5127 . . . . . . . . . . 11
2723, 26nfop 4206 . . . . . . . . . 10
2825, 27nfcxfr 2589 . . . . . . . . 9
2924, 28nffv 5888 . . . . . . . 8
3023, 29nfop 4206 . . . . . . 7
3130nfsn 4060 . . . . . 6
3222, 31nfun 3628 . . . . 5
331, 32nfcxfr 2589 . . . 4
34 nfcv 2591 . . . 4
3533, 34nffv 5888 . . 3
36 bnj1446.13 . . . . 5
37 nfcv 2591 . . . . . . 7
3833, 37nfres 5127 . . . . . 6
3934, 38nfop 4206 . . . . 5
4036, 39nfcxfr 2589 . . . 4
4124, 40nffv 5888 . . 3
4235, 41nfeq 2602 . 2
4342nfri 1927 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wa 370   w3a 982  wal 1435   wceq 1437  wex 1659   wcel 1870  cab 2414   wne 2625  wral 2782  wrex 2783  crab 2786  wsbc 3305   cun 3440   wss 3442  c0 3767  csn 4002  cop 4008  cuni 4222   class class class wbr 4426   cdm 4854   cres 4856   wfn 5596  cfv 5601   c-bnj14 29281   w-bnj15 29285   c-bnj18 29287 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-sbc 3306  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-uni 4223  df-br 4427  df-opab 4485  df-xp 4860  df-res 4866  df-iota 5565  df-fv 5609 This theorem is referenced by:  bnj1450  29647  bnj1463  29652
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