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

Theorem bj-bialal 33939
Description: When 𝜑 is substituted for 𝜓, both sides express a form of nonfreeness. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-bialal (∀𝑥(∀𝑥𝜑𝜓) ↔ (∀𝑥𝜑 → ∀𝑥𝜓))

Proof of Theorem bj-bialal
StepHypRef Expression
1 nfa1 2146 . 2 𝑥𝑥𝜑
2119.21 2197 1 (∀𝑥(∀𝑥𝜑𝜓) ↔ (∀𝑥𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wal 1526
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-10 2136  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-or 842  df-ex 1772  df-nf 1776
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator