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Metamath Proof Explorer

Theorem 19.35i

Description: Inference associated with 19.35 . (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypothesis 19.35i.1 ⊢ ∃ 𝑥 ( 𝜑 → 𝜓 )
Assertion 19.35i ( ∀ 𝑥 𝜑 → ∃ 𝑥 𝜓 )

Proof

Step Hyp Ref Expression
1 19.35i.1 ⊢ ∃ 𝑥 ( 𝜑 → 𝜓 )
2 19.35 ⊢ ( ∃ 𝑥 ( 𝜑 → 𝜓 ) ↔ ( ∀ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) )
3 1 2 mpbi ⊢ ( ∀ 𝑥 𝜑 → ∃ 𝑥 𝜓 )