Theorem mobii 1979

Description: Formula-building rule for "at most one" quantifier (inference rule). (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 1978	. 2 |- ( T. -> ( E* x ps <-> E* x ch ) )
4	3	trud 1294	1 |- ( E* x ps <-> E* x ch )

Syntax hints:   <-> wb 103   T. wtru 1286   E*wmo 1943

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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-eu 1945  df-mo 1946

This theorem is referenced by:  moaneu  2018  moanmo  2019  2moswapdc  2032  2exeu  2034  rmobiia  2544  rmov  2620  euxfr2dc  2778  rmoan  2791  2rmorex  2797  mosn  3437  dffun9  4960  funopab  4965  funco  4970  funcnv2  4990  funcnv  4991  fun2cnv  4994  fncnv  4996  imadif  5010  fnres  5046  ovi3  5668  oprabex3  5787  frecuzrdgtcl  9494  frecuzrdgfunlem  9501