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Theorem sbnf2 2108
 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 1612 . 2
2 df-nf 1545 . . . . 5
3 sbhb 2107 . . . . . 6
43albii 1566 . . . . 5
5 alcom 1737 . . . . 5
62, 4, 53bitri 262 . . . 4
7 nfv 1619 . . . . . . 7
87sb8 2092 . . . . . 6
9 nfs1v 2106 . . . . . . . 8
109sblim 2068 . . . . . . 7
1110albii 1566 . . . . . 6
128, 11bitri 240 . . . . 5
1312albii 1566 . . . 4
14 alcom 1737 . . . 4
156, 13, 143bitri 262 . . 3
16 sbhb 2107 . . . . . 6
1716albii 1566 . . . . 5
18 alcom 1737 . . . . 5
192, 17, 183bitri 262 . . . 4
20 nfv 1619 . . . . . . 7
2120sb8 2092 . . . . . 6
22 nfs1v 2106 . . . . . . . 8
2322sblim 2068 . . . . . . 7
2423albii 1566 . . . . . 6
2521, 24bitri 240 . . . . 5
2625albii 1566 . . . 4
2719, 26bitri 240 . . 3
2815, 27anbi12i 678 . 2
29 anidm 625 . 2
301, 28, 293bitr2ri 265 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wnf 1544  wsb 1648 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 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649 This theorem is referenced by:  sbnfc2  3196
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