Theorem rmoanid

Description: Cancellation law for restricted at-most-one quantification. (Contributed by Peter Mazsa, 24-May-2018)

	Ref	Expression
Assertion	rmoanid	|- ( E* x e. A ( x e. A /\ ph ) <-> E* x e. A ph )

Proof

Step	Hyp	Ref	Expression
1		anabs5	|- ( ( x e. A /\ ( x e. A /\ ph ) ) <-> ( x e. A /\ ph ) )
2	1	mobii	|- ( E* x ( x e. A /\ ( x e. A /\ ph ) ) <-> E* x ( x e. A /\ ph ) )
3		df-rmo	|- ( E* x e. A ( x e. A /\ ph ) <-> E* x ( x e. A /\ ( x e. A /\ ph ) ) )
4		df-rmo	|- ( E* x e. A ph <-> E* x ( x e. A /\ ph ) )
5	2 3 4	3bitr4i	|- ( E* x e. A ( x e. A /\ ph ) <-> E* x e. A ph )