Theorem equvinva

Description: A modified version of the forward implication of equvinv adapted to common usage. (Contributed by Wolf Lammen, 8-Sep-2018)

	Ref	Expression
Assertion	equvinva	|- ( x = y -> E. z ( x = z /\ y = z ) )

Proof

Step	Hyp	Ref	Expression
1		ax6evr	|- E. z y = z
2		equtr	|- ( x = y -> ( y = z -> x = z ) )
3	2	ancrd	|- ( x = y -> ( y = z -> ( x = z /\ y = z ) ) )
4	3	eximdv	|- ( x = y -> ( E. z y = z -> E. z ( x = z /\ y = z ) ) )
5	1 4	mpi	|- ( x = y -> E. z ( x = z /\ y = z ) )