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Theorem moanim 1974
 Description: Introduction of a conjunct into "at most one" quantifier. (Contributed by NM, 3-Dec-2001.)
Hypothesis
Ref Expression
moanim.1
Assertion
Ref Expression
moanim

Proof of Theorem moanim
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 anandi 524 . . . . 5
21imbi1i 227 . . . 4
3 impexp 250 . . . 4
4 sban 1829 . . . . . . 7
5 moanim.1 . . . . . . . . 9
65sbf 1660 . . . . . . . 8
76anbi1i 431 . . . . . . 7
84, 7bitr2i 174 . . . . . 6
98anbi2i 430 . . . . 5
109imbi1i 227 . . . 4
112, 3, 103bitr3i 199 . . 3
12112albii 1360 . 2
13519.21 1475 . . 3
14 19.21v 1753 . . . 4
1514albii 1359 . . 3
16 ax-17 1419 . . . . 5
1716mo3h 1953 . . . 4
1817imbi2i 215 . . 3
1913, 15, 183bitr4ri 202 . 2
20 ax-17 1419 . . 3
2120mo3h 1953 . 2
2212, 19, 213bitr4ri 202 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241  wnf 1349  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:  moanimv  1975  moaneu  1976  moanmo  1977
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