Theorem exbiii 43007

Description: Inference associated with exbii 1878. Weaker version of eximii 1867. (Contributed by SN, 14-Oct-2025.)

Hypotheses

Ref	Expression
exbiii.1	⊢ ∃𝑥𝜑
exbiii.2	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
exbiii	⊢ ∃𝑥𝜓

Proof of Theorem exbiii

Step	Hyp	Ref	Expression
1		exbiii.1	. 2 ⊢ ∃𝑥𝜑
2		exbiii.2	. . 3 ⊢ (𝜑 ↔ 𝜓)
3	2	biimpi 219	. 2 ⊢ (𝜑 → 𝜓)
4	1, 3	eximii 1867	1 ⊢ ∃𝑥𝜓

This proof depends on syntax axioms:   ↔ wb 209  ∃wex 1809

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839

This proof depends on definitions:  df-bi 210  df-ex 1810

This theorem is used by: (None)