Theorem alrot3 1738

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

Assertion

Ref	Expression
alrot3	|- (A.xA.yA.zph <-> A.yA.zA.xph)

Proof of Theorem alrot3

Step	Hyp	Ref	Expression
1		alcom 1737	. 2 |- (A.xA.yA.zph <-> A.yA.xA.zph)
2		alcom 1737	. . 3 |- (A.xA.zph <-> A.zA.xph)
3	2	albii 1566	. 2 |- (A.yA.xA.zph <-> A.yA.zA.xph)
4	1, 3	bitri 240	1 |- (A.xA.yA.zph <-> A.yA.zA.xph)

Syntax hints:   <-> wb 176  A.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