Theorem alrot3 2161

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 2160	. 2 ⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑥∀𝑧𝜑)
2		alcom 2160	. . 3 ⊢ (∀𝑥∀𝑧𝜑 ↔ ∀𝑧∀𝑥𝜑)
3	2	albii 1827	. 2 ⊢ (∀𝑦∀𝑥∀𝑧𝜑 ↔ ∀𝑦∀𝑧∀𝑥𝜑)
4	1, 3	bitri 278	1 ⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑧∀𝑥𝜑)

Syntax hints:   ↔ wb 209  ∀wal 1541

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-11 2158

This theorem depends on definitions:  df-bi 210

This theorem is referenced by:  alrot4  2162  nfnid  5268  raliunxp  5708  dff13  7067  cosscnvssid3  36331  undmrnresiss  40888