Metamath Proof Explorer


Theorem exlimdvv

Description: Deduction form of Theorem 19.23 of Margaris p. 90, see 19.23 . (Contributed by NM, 31-Jul-1995)

Ref Expression
Hypothesis exlimdvv.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion exlimdvv ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 𝜓 → 𝜒 ) )

Proof

Step Hyp Ref Expression
1 exlimdvv.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2 1 exlimdv ⊢ ( 𝜑 → ( ∃ 𝑦 𝜓 → 𝜒 ) )
3 2 exlimdv ⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 𝜓 → 𝜒 ) )