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Metamath Proof Explorer

Theorem 19.8v

Description: Version of 19.8a with a disjoint variable condition, requiring fewer axioms. Converse of ax5e . (Contributed by BJ, 12-Mar-2020)

Ref Expression
Assertion 19.8v ( 𝜑 → ∃ 𝑥 𝜑 )

Proof

Step Hyp Ref Expression
1 ax-5 ⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
2 1 19.8w ⊢ ( 𝜑 → ∃ 𝑥 𝜑 )