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	⊢ Ⅎ 𝑥 𝜑
	exlimiieq1.2	⊢ ( 𝑥 = 𝑦 → 𝜑 )
Assertion	exlimiieq1	⊢ 𝜑

Proof

Step	Hyp	Ref	Expression
1		exlimiieq1.1	⊢ Ⅎ 𝑥 𝜑
2		exlimiieq1.2	⊢ ( 𝑥 = 𝑦 → 𝜑 )
3		ax6e	⊢ ∃ 𝑥 𝑥 = 𝑦
4	1 2 3	exlimii	⊢ 𝜑