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	⊢ Ⅎ 𝑦 𝜑
	exlimiieq2.2	⊢ ( 𝑥 = 𝑦 → 𝜑 )
Assertion	exlimiieq2	⊢ 𝜑

Proof

Step	Hyp	Ref	Expression
1		exlimiieq2.1	⊢ Ⅎ 𝑦 𝜑
2		exlimiieq2.2	⊢ ( 𝑥 = 𝑦 → 𝜑 )
3		ax6er	⊢ ∃ 𝑦 𝑥 = 𝑦
4	1 2 3	exlimii	⊢ 𝜑