Theorem mobii 2091

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

Step	Hyp	Ref	Expression
1		mobii.1	. . . 4 |- ( ps <-> ch )
2	1	a1i 9	. . 3 |- ( T. -> ( ps <-> ch ) )
3	2	mobidv 2090	. 2 |- ( T. -> ( E* x ps <-> E* x ch ) )
4	3	mptru 1382	1 |- ( E* x ps <-> E* x ch )

Syntax hints:   <-> wb 105   T. wtru 1374   E*wmo 2055

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-17 1549  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-eu 2057  df-mo 2058

This theorem is referenced by:  moaneu  2130  moanmo  2131  2moswapdc  2144  2exeu  2146  rmobiia  2696  rmov  2792  euxfr2dc  2958  rmoan  2973  2rmorex  2979  mosn  3669  dffun9  5301  funopab  5307  funco  5312  funcnv2  5335  funcnv  5336  fun2cnv  5339  fncnv  5341  imadif  5355  fnres  5394  ovi3  6085  oprabex3  6216  axaddf  7983  axmulf  7984  frecuzrdgtcl  10559  frecuzrdgfunlem  10566  fsum3  11731