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Theorem sbnfc2 3196
 Description: Two ways of expressing " is (effectively) not free in ." (Contributed by Mario Carneiro, 14-Oct-2016.)
Assertion
Ref Expression
sbnfc2
Distinct variable groups:   ,,   ,,
Allowed substitution hint:   ()

Proof of Theorem sbnfc2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2862 . . . . 5
2 csbtt 3148 . . . . 5
31, 2mpan 651 . . . 4
4 vex 2862 . . . . 5
5 csbtt 3148 . . . . 5
64, 5mpan 651 . . . 4
73, 6eqtr4d 2388 . . 3
87alrimivv 1632 . 2
9 nfv 1619 . . 3
10 eleq2 2414 . . . . . 6
11 sbsbc 3050 . . . . . . 7
12 sbcel2g 3157 . . . . . . . 8
131, 12ax-mp 8 . . . . . . 7
1411, 13bitri 240 . . . . . 6
15 sbsbc 3050 . . . . . . 7
16 sbcel2g 3157 . . . . . . . 8
174, 16ax-mp 8 . . . . . . 7
1815, 17bitri 240 . . . . . 6
1910, 14, 183bitr4g 279 . . . . 5
20192alimi 1560 . . . 4
21 sbnf2 2108 . . . 4
2220, 21sylibr 203 . . 3
239, 22nfcd 2484 . 2
248, 23impbii 180 1
 Colors of variables: wff setvar class Syntax hints:   wb 176  wal 1540  wnf 1544   wceq 1642  wsb 1648   wcel 1710  wnfc 2476  cvv 2859  wsbc 3046  csb 3136 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-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: (None)
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