Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbnf2 Structured version   Unicode version

Theorem sbnf2 2183
 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 1622 . 2
2 df-nf 1554 . . . . 5
3 sbhb 2182 . . . . . 6
43albii 1575 . . . . 5
5 alcom 1752 . . . . 5
62, 4, 53bitri 263 . . . 4
7 nfv 1629 . . . . . . 7
87sb8 2167 . . . . . 6
9 nfs1v 2181 . . . . . . . 8
109sblim 2142 . . . . . . 7
1110albii 1575 . . . . . 6
128, 11bitri 241 . . . . 5
1312albii 1575 . . . 4
14 alcom 1752 . . . 4
156, 13, 143bitri 263 . . 3
16 sbhb 2182 . . . . . 6
1716albii 1575 . . . . 5
18 alcom 1752 . . . . 5
192, 17, 183bitri 263 . . . 4
20 nfv 1629 . . . . . . 7
2120sb8 2167 . . . . . 6
22 nfs1v 2181 . . . . . . . 8
2322sblim 2142 . . . . . . 7
2423albii 1575 . . . . . 6
2521, 24bitri 241 . . . . 5
2625albii 1575 . . . 4
2719, 26bitri 241 . . 3
2815, 27anbi12i 679 . 2
29 anidm 626 . 2
301, 28, 293bitr2ri 266 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wnf 1553  wsb 1658 This theorem is referenced by:  sbnfc2  3301  nfnid  4385 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
 Copyright terms: Public domain W3C validator