Theorem exlimiieq1

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

	Ref	Expression
Hypotheses	exlimiieq1.1	$$⊢Ⅎx\phi$$
	exlimiieq1.2	$$⊢x=y\to \phi$$
Assertion	exlimiieq1	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		exlimiieq1.1	$$⊢Ⅎx\phi$$
2		exlimiieq1.2	$$⊢x=y\to \phi$$
3		ax6e	$$⊢\exists xx=y$$
4	1 2 3	exlimii	$$⊢\phi$$