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Theorem mobidv 2178
Description: Formula-building rule for "at most one" quantifier (deduction rule). (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 1605 . 2  |-  F/ x ph
2 mobidv.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2mobid 2177 1  |-  ( ph  ->  ( E* x ps  <->  E* x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   E*wmo 2144
This theorem is referenced by:  mobii  2179  mosubopt  4264  dffun6f  5269  funmo  5271  caovmo  6057  1stconst  6207  2ndconst  6208  brdom3  8153  brdom6disj  8157  imasaddfnlem  13430  imasvscafn  13439  hausflim  17676  hausflf  17692  haustsms  17818  limcmo  19232  perfdvf  19253  funressnfv  27403
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-ex 1529  df-nf 1532  df-eu 2147  df-mo 2148
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