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

Theorem reurex 2580
Description: Restricted unique existence implies restricted existence. (Contributed by NM, 19-Aug-1999.)
Assertion
Ref Expression
reurex (∃!𝑥𝐴 𝜑 → ∃𝑥𝐴 𝜑)

Proof of Theorem reurex
StepHypRef Expression
1 reu5 2579 . 2 (∃!𝑥𝐴 𝜑 ↔ (∃𝑥𝐴 𝜑 ∧ ∃*𝑥𝐴 𝜑))
21simplbi 268 1 (∃!𝑥𝐴 𝜑 → ∃𝑥𝐴 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wrex 2360  ∃!wreu 2361  ∃*wrmo 2362
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952  df-rex 2365  df-reu 2366  df-rmo 2367
This theorem is referenced by:  reu3  2805  prsrriota  7331  elrealeu  7365
  Copyright terms: Public domain W3C validator