Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-nexdh2 Structured version   Visualization version   GIF version

Theorem bj-nexdh2 31791
Description: Uncurried form of bj-nexdh 31790. (Contributed by BJ, 6-May-2019.)
Assertion
Ref Expression
bj-nexdh2 ((∀𝑥(𝜑 → ¬ 𝜓) ∧ (𝜒 → ∀𝑥𝜑)) → (𝜒 → ¬ ∃𝑥𝜓))

Proof of Theorem bj-nexdh2
StepHypRef Expression
1 bj-nexdh 31790 . 2 (∀𝑥(𝜑 → ¬ 𝜓) → ((𝜒 → ∀𝑥𝜑) → (𝜒 → ¬ ∃𝑥𝜓)))
21imp 444 1 ((∀𝑥(𝜑 → ¬ 𝜓) ∧ (𝜒 → ∀𝑥𝜑)) → (𝜒 → ¬ ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 383  wal 1473  wex 1695
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 1728
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator