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Theorem bnj1448 29416
 Description: Technical lemma for bnj60 29431. 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
bnj1448.1
bnj1448.2
bnj1448.3
bnj1448.4
bnj1448.5
bnj1448.6
bnj1448.7
bnj1448.8
bnj1448.9
bnj1448.10
bnj1448.11
bnj1448.12
bnj1448.13
Assertion
Ref Expression
bnj1448
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,,,)   (,,,,)   (,,,,)   (,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,)   (,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)

Proof of Theorem bnj1448
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj1448.12 . . . . 5
2 bnj1448.10 . . . . . . 7
3 bnj1448.9 . . . . . . . . . 10
43bnj1317 29193 . . . . . . . . 9
54nfcii 2563 . . . . . . . 8
65nfuni 4021 . . . . . . 7
72, 6nfcxfr 2569 . . . . . 6
8 nfcv 2572 . . . . . . . 8
9 nfcv 2572 . . . . . . . . 9
10 bnj1448.11 . . . . . . . . . 10
11 nfcv 2572 . . . . . . . . . . . 12
127, 11nfres 5148 . . . . . . . . . . 11
138, 12nfop 4000 . . . . . . . . . 10
1410, 13nfcxfr 2569 . . . . . . . . 9
159, 14nffv 5735 . . . . . . . 8
168, 15nfop 4000 . . . . . . 7
1716nfsn 3866 . . . . . 6
187, 17nfun 3503 . . . . 5
191, 18nfcxfr 2569 . . . 4
20 nfcv 2572 . . . 4
2119, 20nffv 5735 . . 3
22 bnj1448.13 . . . . 5
23 nfcv 2572 . . . . . . 7
2419, 23nfres 5148 . . . . . 6
2520, 24nfop 4000 . . . . 5
2622, 25nfcxfr 2569 . . . 4
279, 26nffv 5735 . . 3
2821, 27nfeq 2579 . 2
2928nfri 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 2422   wne 2599  wral 2705  wrex 2706  crab 2709  wsbc 3161   cun 3318   wss 3320  c0 3628  csn 3814  cop 3817  cuni 4015   class class class wbr 4212   cdm 4878   cres 4880   wfn 5449  cfv 5454   c-bnj14 29052   w-bnj15 29056   c-bnj18 29058 This theorem is referenced by:  bnj1450  29419  bnj1463  29424 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-xp 4884  df-res 4890  df-iota 5418  df-fv 5462
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