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Metamath Proof Explorer

Theorem exlimivv

Description: Inference form of Theorem 19.23 of Margaris p. 90, see 19.23 . (Contributed by NM, 1-Aug-1995)

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

Proof

Step Hyp Ref Expression
1 exlimivv.1 ⊢ ( 𝜑 → 𝜓 )
2 1 exlimiv ⊢ ( ∃ 𝑦 𝜑 → 𝜓 )
3 2 exlimiv ⊢ ( ∃ 𝑥 ∃ 𝑦 𝜑 → 𝜓 )