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Theorem mobid 1935
 Description: Formula-building rule for "at most one" quantifier (deduction rule). (Contributed by NM, 8-Mar-1995.)
Hypotheses
Ref Expression
mobid.1
mobid.2
Assertion
Ref Expression
mobid

Proof of Theorem mobid
StepHypRef Expression
1 mobid.1 . . . 4
2 mobid.2 . . . 4
31, 2exbid 1507 . . 3
41, 2eubid 1907 . . 3
53, 4imbi12d 223 . 2
6 df-mo 1904 . 2
7 df-mo 1904 . 2
85, 6, 73bitr4g 212 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wnf 1349  wex 1381  weu 1900  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-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-eu 1903  df-mo 1904 This theorem is referenced by:  mobidv  1936  rmobida  2496  rmoeq1f  2504
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