Theorem mobidv 1977

Description: Formula-building rule for "at most one" quantifier (deduction rule). (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 1461	. 2 |- F/ x ph
2		mobidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	mobid 1976	1 |- ( ph -> ( E* x ps <-> E* x ch ) )

Syntax hints:   -> wi 4   <-> wb 103   E*wmo 1942

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 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-17 1459  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-eu 1944  df-mo 1945

This theorem is referenced by:  mobii  1978  mosubopt  4423  dffun6f  4935  funmo  4937  1stconst  5862  2ndconst  5863