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Theorem sbmo 1959
 Description: Substitution into "at most one". (Contributed by Jeff Madsen, 2-Sep-2009.)
Assertion
Ref Expression
sbmo
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sbmo
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1421 . . . . . 6
21sblim 1831 . . . . 5
3 sban 1829 . . . . . 6
43imbi1i 227 . . . . 5
5 sbcom2 1863 . . . . . . 7
65anbi2i 430 . . . . . 6
76imbi1i 227 . . . . 5
82, 4, 73bitri 195 . . . 4
98sbalv 1881 . . 3
109sbalv 1881 . 2
11 nfv 1421 . . . 4
1211mo3 1954 . . 3
1312sbbii 1648 . 2
14 nfv 1421 . . 3
1514mo3 1954 . 2
1610, 13, 153bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wceq 1243  wsb 1645  wmo 1901 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-bndl 1399  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  df-eu 1903  df-mo 1904 This theorem is referenced by: (None)
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