Theorem exbiii

Description: Inference associated with exbii . Weaker version of eximii . (Contributed by SN, 14-Oct-2025)

	Ref	Expression
Hypotheses	exbiii.1	⊢ ∃ 𝑥 𝜑
	exbiii.2	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	exbiii	⊢ ∃ 𝑥 𝜓

Proof

Step	Hyp	Ref	Expression
1		exbiii.1	⊢ ∃ 𝑥 𝜑
2		exbiii.2	⊢ ( 𝜑 ↔ 𝜓 )
3	2	biimpi	⊢ ( 𝜑 → 𝜓 )
4	1 3	eximii	⊢ ∃ 𝑥 𝜓