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Theorem csbiebt 3172
Description: Conversion of implicit substitution to explicit substitution into a class. (Closed theorem version of csbiegf 3176.) (Contributed by NM, 11-Nov-2005.)
Assertion
Ref Expression
csbiebt  F/_
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem csbiebt
StepHypRef Expression
1 elex 2867 . 2
2 spsbc 3058 . . . . 5  [.  ].
32adantr 451 . . . 4  F/_  [.  ].
4 simpl 443 . . . . 5  F/_
5 biimt 325 . . . . . . 7
6 csbeq1a 3144 . . . . . . . 8
76eqeq1d 2361 . . . . . . 7
85, 7bitr3d 246 . . . . . 6
98adantl 452 . . . . 5 
F/_
10 nfv 1619 . . . . . 6  F/
11 nfnfc1 2492 . . . . . 6  F/ F/_
1210, 11nfan 1824 . . . . 5  F/ 
F/_
13 nfcsb1v 3168 . . . . . . 7  F/_
1413a1i 10 . . . . . 6  F/_  F/_
15 simpr 447 . . . . . 6  F/_  F/_
1614, 15nfeqd 2503 . . . . 5  F/_ 
F/
174, 9, 12, 16sbciedf 3081 . . . 4  F/_  [.  ].
183, 17sylibd 205 . . 3  F/_
1913a1i 10 . . . . . . . 8  F/_  F/_
20 id 19 . . . . . . . 8  F/_  F/_
2119, 20nfeqd 2503 . . . . . . 7  F/_  F/
2211, 21nfan1 1881 . . . . . 6  F/ F/_
237biimprcd 216 . . . . . . 7
2423adantl 452 . . . . . 6 
F/_
2522, 24alrimi 1765 . . . . 5 
F/_
2625ex 423 . . . 4  F/_
2726adantl 452 . . 3  F/_
2818, 27impbid 183 . 2  F/_
291, 28sylan 457 1  F/_
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358  wal 1540   wceq 1642   wcel 1710   F/_wnfc 2476  cvv 2859   [.wsbc 3046  csb 3136
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137
This theorem is referenced by:  csbiedf  3173  csbieb  3174  csbiegf  3176
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