ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  alrimdh GIF version

Theorem alrimdh 1384
Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Hypotheses
Ref Expression
alrimdh.1 (𝜑 → ∀𝑥𝜑)
alrimdh.2 (𝜓 → ∀𝑥𝜓)
alrimdh.3 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
alrimdh (𝜑 → (𝜓 → ∀𝑥𝜒))

Proof of Theorem alrimdh
StepHypRef Expression
1 alrimdh.2 . 2 (𝜓 → ∀𝑥𝜓)
2 alrimdh.1 . . 3 (𝜑 → ∀𝑥𝜑)
3 alrimdh.3 . . 3 (𝜑 → (𝜓𝜒))
42, 3alimdh 1372 . 2 (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
51, 4syl5 32 1 (𝜑 → (𝜓 → ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1352  ax-gen 1354
This theorem is referenced by:  nfimd  1493  alrimdv  1772  moexexdc  2000
  Copyright terms: Public domain W3C validator