Theorem 3bitrrd 544

Description: Deduction from transitivity of biconditional.

Hypotheses

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

Assertion

Ref	Expression
3bitrrd	|- (ph -> (ta <-> ps))

Proof of Theorem 3bitrrd

Step	Hyp	Ref	Expression
1		3bitrd.3	. 2 |- (ph -> (th <-> ta))
2		3bitrd.1	. . 3 |- (ph -> (ps <-> ch))
3		3bitrd.2	. . 3 |- (ph -> (ch <-> th))
4	2, 3	bitr2d 528	. 2 |- (ph -> (th <-> ps))
5	1, 4	bitr3d 529	1 |- (ph -> (ta <-> ps))

Syntax hints:   -> wi 3   <-> wb 146

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

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