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

Theorem exlimd 1533
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 1457 . 2 (𝜑 → ∀𝑥𝜑)
3 exlimd.2 . . 3 𝑥𝜒
43nfri 1457 . 2 (𝜒 → ∀𝑥𝜒)
5 exlimd.3 . 2 (𝜑 → (𝜓𝜒))
62, 4, 5exlimdh 1532 1 (𝜑 → (∃𝑥𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1394  wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-5 1381  ax-gen 1383  ax-ie2 1428  ax-4 1445
This theorem depends on definitions:  df-bi 115  df-nf 1395
This theorem is referenced by:  exlimdd  1800  ceqsalg  2647  copsex2t  4063  alxfr  4274  mosubopt  4491  ovmpt2df  5758  ovi3  5763  fsum2dlemstep  10791  bj-exlimmp  11327
  Copyright terms: Public domain W3C validator