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

Theorem eubidv 1956
Description: Formula-building rule for unique existential quantifier (deduction form). (Contributed by NM, 9-Jul-1994.)
Hypothesis
Ref Expression
eubidv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
eubidv (𝜑 → (∃!𝑥𝜓 ↔ ∃!𝑥𝜒))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)

Proof of Theorem eubidv
StepHypRef Expression
1 nfv 1466 . 2 𝑥𝜑
2 eubidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2eubid 1955 1 (𝜑 → (∃!𝑥𝜓 ↔ ∃!𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  ∃!weu 1948
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-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-eu 1951
This theorem is referenced by:  eubii  1957  eueq2dc  2788  eueq3dc  2789  reuhypd  4291  feu  5187  funfveu  5312  dff4im  5439  acexmid  5643
  Copyright terms: Public domain W3C validator