Theorem alrot3 2024

Description: Theorem *11.21 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
alrot3	⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑧∀𝑥𝜑)

Proof of Theorem alrot3

Step	Hyp	Ref	Expression
1		alcom 2023	. 2 ⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑥∀𝑧𝜑)
2		alcom 2023	. . 3 ⊢ (∀𝑥∀𝑧𝜑 ↔ ∀𝑧∀𝑥𝜑)
3	2	albii 1736	. 2 ⊢ (∀𝑦∀𝑥∀𝑧𝜑 ↔ ∀𝑦∀𝑧∀𝑥𝜑)
4	1, 3	bitri 262	1 ⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑧∀𝑥𝜑)

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