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

Theorem exlimd 1488
Description: Deduction from Theorem 19.9 of [Margaris] p. 89. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof rewritten by Jim Kingdon, 18-Jun-2018.)
Hypotheses
Ref Expression
exlimd.1 𝑥𝜑
exlimd.2 𝑥𝜒
exlimd.3 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
exlimd (𝜑 → (∃𝑥𝜓𝜒))

Proof of Theorem exlimd
StepHypRef Expression
1 exlimd.1 . . 3 𝑥𝜑
21nfri 1412 . 2 (𝜑 → ∀𝑥𝜑)
3 exlimd.2 . . 3 𝑥𝜒
43nfri 1412 . 2 (𝜒 → ∀𝑥𝜒)
5 exlimd.3 . 2 (𝜑 → (𝜓𝜒))
62, 4, 5exlimdh 1487 1 (𝜑 → (∃𝑥𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1349  wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-4 1400
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by:  exlimdd  1752  ceqsalg  2582  copsex2t  3982  alxfr  4193  mosubopt  4405  ovmpt2df  5632  ovi3  5637  bj-exlimmp  9909
  Copyright terms: Public domain W3C validator