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Theorem sbnf2 1857
 Description: Two ways of expressing " is (effectively) not free in ." (Contributed by Gérard Lang, 14-Nov-2013.) (Revised by Mario Carneiro, 6-Oct-2016.)
Assertion
Ref Expression
sbnf2
Distinct variable groups:   ,,   ,,
Allowed substitution hint:   ()

Proof of Theorem sbnf2
StepHypRef Expression
1 2albiim 1377 . 2
2 df-nf 1350 . . . . 5
3 sbhb 1816 . . . . . 6
43albii 1359 . . . . 5
5 alcom 1367 . . . . 5
62, 4, 53bitri 195 . . . 4
7 nfv 1421 . . . . . . 7
87sb8 1736 . . . . . 6
9 nfs1v 1815 . . . . . . . 8
109sblim 1831 . . . . . . 7
1110albii 1359 . . . . . 6
128, 11bitri 173 . . . . 5
1312albii 1359 . . . 4
14 alcom 1367 . . . 4
156, 13, 143bitri 195 . . 3
16 sbhb 1816 . . . . . 6
1716albii 1359 . . . . 5
18 alcom 1367 . . . . 5
192, 17, 183bitri 195 . . . 4
20 nfv 1421 . . . . . . 7
2120sb8 1736 . . . . . 6
22 nfs1v 1815 . . . . . . . 8
2322sblim 1831 . . . . . . 7
2423albii 1359 . . . . . 6
2521, 24bitri 173 . . . . 5
2625albii 1359 . . . 4
2719, 26bitri 173 . . 3
2815, 27anbi12i 433 . 2
29 anidm 376 . 2
301, 28, 293bitr2ri 198 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241  wnf 1349  wsb 1645 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646 This theorem is referenced by:  sbnfc2  2906
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