Theorem alrot3 1478

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 1471	. 2 ⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑥∀𝑧𝜑)
2		alcom 1471	. . 3 ⊢ (∀𝑥∀𝑧𝜑 ↔ ∀𝑧∀𝑥𝜑)
3	2	albii 1463	. 2 ⊢ (∀𝑦∀𝑥∀𝑧𝜑 ↔ ∀𝑦∀𝑧∀𝑥𝜑)
4	1, 3	bitri 183	1 ⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑧∀𝑥𝜑)

Syntax hints:   ↔ wb 104  ∀wal 1346

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  alrot4  1479  raliunxp  4752  dff13  5747