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Theorem mobidv 2035
Description: Formula-building rule for "at most one" quantifier (deduction form). (Contributed by Mario Carneiro, 7-Oct-2016.)
Hypothesis
Ref Expression
mobidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
mobidv  |-  ( ph  ->  ( E* x ps  <->  E* x ch ) )
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)

Proof of Theorem mobidv
StepHypRef Expression
1 nfv 1508 . 2  |-  F/ x ph
2 mobidv.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2mobid 2034 1  |-  ( ph  ->  ( E* x ps  <->  E* x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   E*wmo 2000
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-eu 2002  df-mo 2003
This theorem is referenced by:  mobii  2036  mosubopt  4604  dffun6f  5136  funmo  5138  1stconst  6118  2ndconst  6119  dvfgg  12836
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