Theorem 3bitrri 205

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 4-Aug-2006.)

Hypotheses

Ref	Expression
3bitri.1	|- ( ph <-> ps )
3bitri.2	|- ( ps <-> ch )
3bitri.3	|- ( ch <-> th )

Assertion

Ref	Expression
3bitrri	|- ( th <-> ph )

Proof of Theorem 3bitrri

Step	Hyp	Ref	Expression
1		3bitri.3	. 2 |- ( ch <-> th )
2		3bitri.1	. . 3 |- ( ph <-> ps )
3		3bitri.2	. . 3 |- ( ps <-> ch )
4	2, 3	bitr2i 183	. 2 |- ( ch <-> ph )
5	1, 4	bitr3i 184	1 |- ( th <-> ph )

Syntax hints:   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  reu8  2788  unass  3129  ssin  3188  difab  3233  iunss  3719  poirr  4062  cnvuni  4539  dfco2  4840  dff1o6  5436  elznn0  8366  bj-ssom  10731