Metamath Proof Explorer

Theorem exbi

Description: Theorem 19.18 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion exbi ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( ∃ 𝑥 𝜑 ↔ ∃ 𝑥 𝜓 ) )

Proof

Step Hyp Ref Expression
1 id ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )
2 1 alexbii ⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( ∃ 𝑥 𝜑 ↔ ∃ 𝑥 𝜓 ) )