Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-exalbial Structured version   Visualization version   GIF version

Theorem bj-exalbial 34621
Description: Adding a second quantifier is a tranparent operation, (∃∀ case). (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-exalbial (∃𝑥𝑥𝜑 ↔ ∀𝑥𝜑)

Proof of Theorem bj-exalbial
StepHypRef Expression
1 nfa1 2152 . 2 𝑥𝑥𝜑
2119.9 2203 1 (∃𝑥𝑥𝜑 ↔ ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wal 1541  wex 1787
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-10 2141  ax-12 2175
This theorem depends on definitions:  df-bi 210  df-or 848  df-ex 1788  df-nf 1792
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator