Theorem exlimiieq2

Description: Inferring a theorem when it is implied by an equality which may be true. (Contributed by BJ, 15-Sep-2018) (Revised by BJ, 30-Sep-2018)

	Ref	Expression
Hypotheses	exlimiieq2.1	$$⊢Ⅎy\phi$$
	exlimiieq2.2	$$⊢x=y\to \phi$$
Assertion	exlimiieq2	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		exlimiieq2.1	$$⊢Ⅎy\phi$$
2		exlimiieq2.2	$$⊢x=y\to \phi$$
3		ax6er	$$⊢\exists yx=y$$
4	1 2 3	exlimii	$$⊢\phi$$