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

Theorem exlimdh 1484
Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jan-1997.)
Hypotheses
Ref Expression
exlimdh.1 (φxφ)
exlimdh.2 (χxχ)
exlimdh.3 (φ → (ψχ))
Assertion
Ref Expression
exlimdh (φ → (xψχ))

Proof of Theorem exlimdh
StepHypRef Expression
1 exlimdh.1 . . 3 (φxφ)
2 exlimdh.3 . . 3 (φ → (ψχ))
31, 2alrimih 1355 . 2 (φx(ψχ))
4 exlimdh.2 . . 3 (χxχ)
5419.23h 1384 . 2 (x(ψχ) ↔ (xψχ))
63, 5sylib 127 1 (φ → (xψχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-5 1333  ax-gen 1335  ax-ie2 1380
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  exlimd  1485  exim  1487  exlimdv  1697  equs5  1707  cbvexdh  1798  exists2  1994
  Copyright terms: Public domain W3C validator