Theorem mobidv 2081

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 1542	. 2 |- F/ x ph
2		mobidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	mobid 2080	1 |- ( ph -> ( E* x ps <-> E* x ch ) )

Syntax hints:   -> wi 4   <-> wb 105   E*wmo 2046

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-eu 2048  df-mo 2049

This theorem is referenced by:  mobii  2082  mosubopt  4729  dffun6f  5272  funmo  5274  1stconst  6280  2ndconst  6281  exmidmotap  7330  imasaddfnlemg  12967  dvfgg  14934