Theorem bitr2d 245

Description: Deduction form of bitr2i 241. (Contributed by NM, 9-Jun-2004.)

Hypotheses

Ref	Expression
bitr2d.1	|- (ph -> (ps <-> ch))
bitr2d.2	|- (ph -> (ch <-> th))

Assertion

Ref	Expression
bitr2d	|- (ph -> (th <-> ps))

Proof of Theorem bitr2d

Step	Hyp	Ref	Expression
1		bitr2d.1	. . 3 |- (ph -> (ps <-> ch))
2		bitr2d.2	. . 3 |- (ph -> (ch <-> th))
3	1, 2	bitrd 244	. 2 |- (ph -> (ps <-> th))
4	3	bicomd 192	1 |- (ph -> (th <-> ps))

Syntax hints:   -> wi 4   <-> wb 176

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

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  3bitrrd  271  3bitr2rd  273  pm5.18  345  fnasrn  5418