MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  alrot3 Structured version   Visualization version   GIF version

Theorem alrot3 2024
Description: Theorem *11.21 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
alrot3 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)

Proof of Theorem alrot3
StepHypRef Expression
1 alcom 2023 . 2 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑥𝑧𝜑)
2 alcom 2023 . . 3 (∀𝑥𝑧𝜑 ↔ ∀𝑧𝑥𝜑)
32albii 1736 . 2 (∀𝑦𝑥𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)
41, 3bitri 262 1 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 194  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-11 2020
This theorem depends on definitions:  df-bi 195
This theorem is referenced by:  alrot4  2025  nfnid  4818  raliunxp  5171  dff13  6394  undmrnresiss  36732  ntrneikb  37215  ntrneixb  37216
  Copyright terms: Public domain W3C validator