Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1447 Structured version   Unicode version

Theorem bnj1447 29643
 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
bnj1447.1
bnj1447.2
bnj1447.3
bnj1447.4
bnj1447.5
bnj1447.6
bnj1447.7
bnj1447.8
bnj1447.9
bnj1447.10
bnj1447.11
bnj1447.12
bnj1447.13
Assertion
Ref Expression
bnj1447
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,,,)   (,,,,)   (,,,,)   (,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,)   (,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)

Proof of Theorem bnj1447
StepHypRef Expression
1 bnj1447.12 . . . . 5
2 bnj1447.10 . . . . . . 7
3 bnj1447.9 . . . . . . . . 9
4 nfre1 2893 . . . . . . . . . 10
54nfab 2595 . . . . . . . . 9
63, 5nfcxfr 2589 . . . . . . . 8
76nfuni 4228 . . . . . . 7
82, 7nfcxfr 2589 . . . . . 6
9 nfcv 2591 . . . . . . . 8
10 nfcv 2591 . . . . . . . . 9
11 bnj1447.11 . . . . . . . . . 10
12 nfcv 2591 . . . . . . . . . . . 12
138, 12nfres 5127 . . . . . . . . . . 11
149, 13nfop 4206 . . . . . . . . . 10
1511, 14nfcxfr 2589 . . . . . . . . 9
1610, 15nffv 5888 . . . . . . . 8
179, 16nfop 4206 . . . . . . 7
1817nfsn 4060 . . . . . 6
198, 18nfun 3628 . . . . 5
201, 19nfcxfr 2589 . . . 4
21 nfcv 2591 . . . 4
2220, 21nffv 5888 . . 3
23 bnj1447.13 . . . . 5
24 nfcv 2591 . . . . . . 7
2520, 24nfres 5127 . . . . . 6
2621, 25nfop 4206 . . . . 5
2723, 26nfcxfr 2589 . . . 4
2810, 27nffv 5888 . . 3
2922, 28nfeq 2602 . 2
3029nfri 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-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
 Copyright terms: Public domain W3C validator