Theorem mobidv 2113

Description: Formula-building rule for "at most one" quantifier (deduction form). (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

Step	Hyp	Ref	Expression
1		nfv 1574	. 2 |- F/ x ph
2		mobidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	mobid 2112	1 |- ( ph -> ( E* x ps <-> E* x ch ) )

Syntax hints:   -> wi 4   <-> wb 105   E*wmo 2078

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-eu 2080  df-mo 2081

This theorem is referenced by:  mobii  2114  mosubopt  4783  dffun6f  5330  funmo  5332  1stconst  6365  2ndconst  6366  exmidmotap  7443  imasaddfnlemg  13342  dvfgg  15356