Theorem mobidv

Description: Formula-building rule for the at-most-one quantifier (deduction form). (Contributed by Mario Carneiro, 7-Oct-2016) Reduce axiom dependencies and shorten proof. (Revised by BJ, 7-Oct-2022)

	Ref	Expression
Hypothesis	mobidv.1	|- ( ph -> ( ps <-> ch ) )
Assertion	mobidv	|- ( ph -> ( E* x ps <-> E* x ch ) )

Proof

Step	Hyp	Ref	Expression
1		mobidv.1	|- ( ph -> ( ps <-> ch ) )
2	1	alrimiv	|- ( ph -> A. x ( ps <-> ch ) )
3		mobi	|- ( A. x ( ps <-> ch ) -> ( E* x ps <-> E* x ch ) )
4	2 3	syl	|- ( ph -> ( E* x ps <-> E* x ch ) )