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

Theorem eubiOLD 42054
Description: Obsolete proof of eubi 2584 as of 7-Oct-2022. (Contributed by Andrew Salmon, 11-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
eubiOLD (∀𝑥(𝜑𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))

Proof of Theorem eubiOLD
StepHypRef Expression
1 nfa1 2148 . 2 𝑥𝑥(𝜑𝜓)
2 sp 2176 . 2 (∀𝑥(𝜑𝜓) → (𝜑𝜓))
31, 2eubid 2587 1 (∀𝑥(𝜑𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wal 1537  ∃!weu 2568
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-10 2137  ax-12 2171
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-ex 1783  df-nf 1787  df-mo 2540  df-eu 2569
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator