Theorem dfmo

Description: Rederive df-mo from the old definition moeu . (Contributed by Wolf Lammen, 27-May-2019) (Proof modification is discouraged.) Use df-mo instead. (New usage is discouraged.)

	Ref	Expression
Assertion	dfmo	|- ( E* x ph <-> E. y A. x ( ph -> x = y ) )

Proof

Step	Hyp	Ref	Expression
1		moeu	|- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		eu6	|- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
3	2	imbi2i	|- ( ( E. x ph -> E! x ph ) <-> ( E. x ph -> E. y A. x ( ph <-> x = y ) ) )
4		dfmoeu	|- ( ( E. x ph -> E. y A. x ( ph <-> x = y ) ) <-> E. y A. x ( ph -> x = y ) )
5	1 3 4	3bitri	|- ( E* x ph <-> E. y A. x ( ph -> x = y ) )