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Metamath Proof Explorer

Theorem 19.36i

Description: Inference associated with 19.36 . See 19.36iv for a version requiring fewer axioms. (Contributed by NM, 24-Jun-1993)

Ref Expression
Hypotheses 19.36.1 ⊢ Ⅎ 𝑥 𝜓
19.36i.2 ⊢ ∃ 𝑥 ( 𝜑 → 𝜓 )
Assertion 19.36i ( ∀ 𝑥 𝜑 → 𝜓 )

Proof

Step Hyp Ref Expression
1 19.36.1 ⊢ Ⅎ 𝑥 𝜓
2 19.36i.2 ⊢ ∃ 𝑥 ( 𝜑 → 𝜓 )
3 1 19.36 ⊢ ( ∃ 𝑥 ( 𝜑 → 𝜓 ) ↔ ( ∀ 𝑥 𝜑 → 𝜓 ) )
4 2 3 mpbi ⊢ ( ∀ 𝑥 𝜑 → 𝜓 )