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Metamath Proof Explorer

Theorem bj-exexbiex

Description: Adding a second quantifier over the same variable is a transparent operation, ( E. E. case). (Contributed by BJ, 20-Oct-2019)

Ref Expression
Assertion bj-exexbiex ( ∃ 𝑥 ∃ 𝑥 𝜑 ↔ ∃ 𝑥 𝜑 )

Proof

Step Hyp Ref Expression
1 nfe1 ⊢ Ⅎ 𝑥 ∃ 𝑥 𝜑
2 1 19.9 ⊢ ( ∃ 𝑥 ∃ 𝑥 𝜑 ↔ ∃ 𝑥 𝜑 )