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Theorem sbnf2 1854
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  F/
Distinct variable groups:   ,,   ,,
Allowed substitution hint:   ()

Proof of Theorem sbnf2
StepHypRef Expression
1 2albiim 1374 . 2
2 df-nf 1347 . . . . 5  F/
3 sbhb 1813 . . . . . 6
43albii 1356 . . . . 5
5 alcom 1364 . . . . 5
62, 4, 53bitri 195 . . . 4  F/
7 nfv 1418 . . . . . . 7  F/
87sb8 1733 . . . . . 6
9 nfs1v 1812 . . . . . . . 8  F/
109sblim 1828 . . . . . . 7
1110albii 1356 . . . . . 6
128, 11bitri 173 . . . . 5
1312albii 1356 . . . 4
14 alcom 1364 . . . 4
156, 13, 143bitri 195 . . 3  F/
16 sbhb 1813 . . . . . 6
1716albii 1356 . . . . 5
18 alcom 1364 . . . . 5
192, 17, 183bitri 195 . . . 4  F/
20 nfv 1418 . . . . . . 7  F/
2120sb8 1733 . . . . . 6
22 nfs1v 1812 . . . . . . . 8  F/
2322sblim 1828 . . . . . . 7
2423albii 1356 . . . . . 6
2521, 24bitri 173 . . . . 5
2625albii 1356 . . . 4
2719, 26bitri 173 . . 3  F/
2815, 27anbi12i 433 . 2  F/  F/
29 anidm 376 . 2  F/  F/  F/
301, 28, 293bitr2ri 198 1  F/
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   F/wnf 1346  wsb 1642
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by:  sbnfc2  2900
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