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Theorem sbnf2 2183
Description: Two ways of expressing " is (effectively) not free in ." (Contributed by GĂ©rard Lang, 14-Nov-2013.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 22-Sep-2018.)
Assertion
Ref Expression
sbnf2
Distinct variable groups:   , ,   , ,

Proof of Theorem sbnf2
StepHypRef Expression
1 nfv 1707 . . . . . 6
21sb8e 2168 . . . . 5
3 nfv 1707 . . . . . 6
43sb8 2167 . . . . 5
52, 4imbi12i 326 . . . 4
6 nf2 1960 . . . 4
7 pm11.53v 1764 . . . 4
85, 6, 73bitr4i 277 . . 3
93sb8e 2168 . . . . . 6
101sb8 2167 . . . . . 6
119, 10imbi12i 326 . . . . 5
12 pm11.53v 1764 . . . . 5
1311, 12bitr4i 252 . . . 4
14 alcom 1845 . . . 4
156, 13, 143bitri 271 . . 3
168, 15anbi12i 697 . 2
17 pm4.24 643 . 2
18 2albiim 1700 . 2
1916, 17, 183bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616  [wsb 1739
This theorem is referenced by:  sbnfc2  3854  nfnid  4681
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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