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Theorem sbmo 1956
 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 1418 . . . . . 6
21sblim 1828 . . . . 5
3 sban 1826 . . . . . 6
43imbi1i 227 . . . . 5
5 sbcom2 1860 . . . . . . 7
65anbi2i 430 . . . . . 6
76imbi1i 227 . . . . 5
82, 4, 73bitri 195 . . . 4
98sbalv 1878 . . 3
109sbalv 1878 . 2
11 nfv 1418 . . . 4
1211mo3 1951 . . 3
1312sbbii 1645 . 2
14 nfv 1418 . . 3
1514mo3 1951 . 2
1610, 13, 153bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wceq 1242  wsb 1642  wmo 1898 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-bnd 1396  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  df-eu 1900  df-mo 1901 This theorem is referenced by: (None)
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