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  5300  funopab  5306  funco  5311  funcnv2  5334  funcnv  5335  fun2cnv  5338  fncnv  5340  imadif  5354  fnres  5392  ovi3  6083  oprabex3  6214  axaddf  7981  axmulf  7982  frecuzrdgtcl  10557  frecuzrdgfunlem  10564  fsum3  11698