Theorem mobidv 2055

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 1521	. 2 |- F/ x ph
2		mobidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	mobid 2054	1 |- ( ph -> ( E* x ps <-> E* x ch ) )

Syntax hints:   -> wi 4   <-> wb 104   E*wmo 2020

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-eu 2022  df-mo 2023

This theorem is referenced by:  mobii  2056  mosubopt  4676  dffun6f  5211  funmo  5213  1stconst  6200  2ndconst  6201  dvfgg  13451