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Metamath Proof Explorer

Theorem eximdh

Description: Deduction from Theorem 19.22 of Margaris p. 90. (Contributed by NM, 20-May-1996)

Ref Expression
Hypotheses eximdh.1 ⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
eximdh.2 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion eximdh ( 𝜑 → ( ∃ 𝑥 𝜓 → ∃ 𝑥 𝜒 ) )

Proof

Step Hyp Ref Expression
1 eximdh.1 ⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
2 eximdh.2 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3 2 aleximi ⊢ ( ∀ 𝑥 𝜑 → ( ∃ 𝑥 𝜓 → ∃ 𝑥 𝜒 ) )
4 1 3 syl ⊢ ( 𝜑 → ( ∃ 𝑥 𝜓 → ∃ 𝑥 𝜒 ) )