Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  eubi Structured version   Visualization version   GIF version

Theorem eubi 38116
Description: Theorem *14.271 in [WhiteheadRussell] p. 192. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
eubi (∀𝑥(𝜑𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))

Proof of Theorem eubi
StepHypRef Expression
1 nfa1 2025 . 2 𝑥𝑥(𝜑𝜓)
2 sp 2051 . 2 (∀𝑥(𝜑𝜓) → (𝜑𝜓))
31, 2eubid 2487 1 (∀𝑥(𝜑𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1478  ∃!weu 2469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1702  df-nf 1707  df-eu 2473
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator