Theorem alrot3 1738

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 1737	. 2 ⊢ (∀x∀y∀zφ ↔ ∀y∀x∀zφ)
2		alcom 1737	. . 3 ⊢ (∀x∀zφ ↔ ∀z∀xφ)
3	2	albii 1566	. 2 ⊢ (∀y∀x∀zφ ↔ ∀y∀z∀xφ)
4	1, 3	bitri 240	1 ⊢ (∀x∀y∀zφ ↔ ∀y∀z∀xφ)

Syntax hints:   ↔ wb 176  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-7 1734

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  alrot4  1739  ssrelk  4212  eqrelk  4213  sikexlem  4296  insklem  4305  raliunxp  4824  ssopr  4847  dffun2  5120  fun11  5160