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Theorem bnj1446 29351
 Description: Technical lemma for bnj60 29368. 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 2571 . . . . . . . . . . 11
5 bnj1446.8 . . . . . . . . . . . 12
6 nfcv 2571 . . . . . . . . . . . . 13
7 bnj1446.4 . . . . . . . . . . . . . 14
8 bnj1446.3 . . . . . . . . . . . . . . . . 17
9 nfre1 2754 . . . . . . . . . . . . . . . . . 18
109nfab 2575 . . . . . . . . . . . . . . . . 17
118, 10nfcxfr 2568 . . . . . . . . . . . . . . . 16
1211nfcri 2565 . . . . . . . . . . . . . . 15
13 nfv 1629 . . . . . . . . . . . . . . 15
1412, 13nfan 1846 . . . . . . . . . . . . . 14
157, 14nfxfr 1579 . . . . . . . . . . . . 13
166, 15nfsbc 3174 . . . . . . . . . . . 12
175, 16nfxfr 1579 . . . . . . . . . . 11
184, 17nfrex 2753 . . . . . . . . . 10
1918nfab 2575 . . . . . . . . 9
203, 19nfcxfr 2568 . . . . . . . 8
2120nfuni 4013 . . . . . . 7
222, 21nfcxfr 2568 . . . . . 6
23 nfcv 2571 . . . . . . . 8
24 nfcv 2571 . . . . . . . . 9
25 bnj1446.11 . . . . . . . . . 10
2622, 4nfres 5140 . . . . . . . . . . 11
2723, 26nfop 3992 . . . . . . . . . 10
2825, 27nfcxfr 2568 . . . . . . . . 9
2924, 28nffv 5727 . . . . . . . 8
3023, 29nfop 3992 . . . . . . 7
3130nfsn 3858 . . . . . 6
3222, 31nfun 3495 . . . . 5
331, 32nfcxfr 2568 . . . 4
34 nfcv 2571 . . . 4
3533, 34nffv 5727 . . 3
36 bnj1446.13 . . . . 5
37 nfcv 2571 . . . . . . 7
3833, 37nfres 5140 . . . . . 6
3934, 38nfop 3992 . . . . 5
4036, 39nfcxfr 2568 . . . 4
4124, 40nffv 5727 . . 3
4235, 41nfeq 2578 . 2
4342nfri 1778 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   w3a 936  wal 1549  wex 1550   wceq 1652   wcel 1725  cab 2421   wne 2598  wral 2697  wrex 2698  crab 2701  wsbc 3153   cun 3310   wss 3312  c0 3620  csn 3806  cop 3809  cuni 4007   class class class wbr 4204   cdm 4870   cres 4872   wfn 5441  cfv 5446   c-bnj14 28989   w-bnj15 28993   c-bnj18 28995 This theorem is referenced by:  bnj1450  29356  bnj1463  29361 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-xp 4876  df-res 4882  df-iota 5410  df-fv 5454
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