Theorem bj-nexdh2 34547

Description: Uncurried (imported) form of bj-nexdh 34546. (Contributed by BJ, 6-May-2019.)

Assertion

Ref	Expression
bj-nexdh2	⊢ ((∀𝑥(𝜑 → ¬ 𝜓) ∧ (𝜒 → ∀𝑥𝜑)) → (𝜒 → ¬ ∃𝑥𝜓))

Proof of Theorem bj-nexdh2

Step	Hyp	Ref	Expression
1		bj-nexdh 34546	. 2 ⊢ (∀𝑥(𝜑 → ¬ 𝜓) → ((𝜒 → ∀𝑥𝜑) → (𝜒 → ¬ ∃𝑥𝜓)))
2	1	imp 410	1 ⊢ ((∀𝑥(𝜑 → ¬ 𝜓) ∧ (𝜒 → ∀𝑥𝜑)) → (𝜒 → ¬ ∃𝑥𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 399  ∀wal 1541  ∃wex 1787

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 1817

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788

This theorem is referenced by: (None)