Theorem 3bitr2ri 208

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

Hypotheses

Ref	Expression
3bitr2i.1	|- ( ph <-> ps )
3bitr2i.2	|- ( ch <-> ps )
3bitr2i.3	|- ( ch <-> th )

Assertion

Ref	Expression
3bitr2ri	|- ( th <-> ph )

Proof of Theorem 3bitr2ri

Step	Hyp	Ref	Expression
1		3bitr2i.1	. . 3 |- ( ph <-> ps )
2		3bitr2i.2	. . 3 |- ( ch <-> ps )
3	1, 2	bitr4i 186	. 2 |- ( ph <-> ch )
4		3bitr2i.3	. 2 |- ( ch <-> th )
5	3, 4	bitr2i 184	1 |- ( th <-> ph )

Syntax hints:   <-> wb 104

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

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  sbnf2  1969  ssrab  3220  rabn0m  3436  unidif0  4146  relop  4754  dmopab3  4817  issref  4986  fununi  5256  cnvoprab  6202  ssfirab  6899