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

Theorem alrimdv 1804
Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 10-Feb-1997.)
Hypothesis
Ref Expression
alrimdv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
alrimdv (𝜑 → (𝜓 → ∀𝑥𝜒))
Distinct variable groups:   𝜑,𝑥   𝜓,𝑥
Allowed substitution hint:   𝜒(𝑥)

Proof of Theorem alrimdv
StepHypRef Expression
1 ax-17 1464 . 2 (𝜑 → ∀𝑥𝜑)
2 ax-17 1464 . 2 (𝜓 → ∀𝑥𝜓)
3 alrimdv.1 . 2 (𝜑 → (𝜓𝜒))
41, 2, 3alrimdh 1413 1 (𝜑 → (𝜓 → ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1287
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1381  ax-gen 1383  ax-17 1464
This theorem is referenced by:  funcnvuni  5069  fliftfun  5557  findcard  6584  findcard2  6585  findcard2s  6586  genprndl  7059  genprndu  7060  bj-inf2vnlem2  11523
  Copyright terms: Public domain W3C validator