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Theorem mobii 1985
Description: Formula-building rule for "at most one" quantifier (inference form). (Contributed by NM, 9-Mar-1995.) (Revised by Mario Carneiro, 17-Oct-2016.)
Hypothesis
Ref Expression
mobii.1  |-  ( ps  <->  ch )
Assertion
Ref Expression
mobii  |-  ( E* x ps  <->  E* x ch )

Proof of Theorem mobii
StepHypRef Expression
1 mobii.1 . . . 4  |-  ( ps  <->  ch )
21a1i 9 . . 3  |-  ( T. 
->  ( ps  <->  ch )
)
32mobidv 1984 . 2  |-  ( T. 
->  ( E* x ps  <->  E* x ch ) )
43mptru 1298 1  |-  ( E* x ps  <->  E* x ch )
Colors of variables: wff set class
Syntax hints:    <-> wb 103   T. wtru 1290   E*wmo 1949
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-eu 1951  df-mo 1952
This theorem is referenced by:  moaneu  2024  moanmo  2025  2moswapdc  2038  2exeu  2040  rmobiia  2556  rmov  2639  euxfr2dc  2798  rmoan  2813  2rmorex  2819  mosn  3474  dffun9  5030  funopab  5035  funco  5040  funcnv2  5060  funcnv  5061  fun2cnv  5064  fncnv  5066  imadif  5080  fnres  5116  ovi3  5763  oprabex3  5882  frecuzrdgtcl  9784  frecuzrdgfunlem  9791  fisum  10742
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