Theorem syl5rbb 411

Description: A syllogism inference from two biconditionals.

Hypotheses

Ref	Expression
syl5rbb.1	|- (ph -> (ps <-> ch))
syl5rbb.2	|- (th <-> ps)

Assertion

Ref	Expression
syl5rbb	|- (ph -> (ch <-> th))

Proof of Theorem syl5rbb

Step	Hyp	Ref	Expression
1		syl5rbb.1	. . 3 |- (ph -> (ps <-> ch))
2		syl5rbb.2	. . 3 |- (th <-> ps)
3	1, 2	syl5bb 410	. 2 |- (ph -> (th <-> ch))
4	3	bicomd 399	1 |- (ph -> (ch <-> th))

Syntax hints:   -> wi 2   <-> wb 127

This theorem is referenced by:  syl5rbbr 413  fnresdisj 2732  f1oiso 2942  rdglim2 2987  1idpr 3927

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

This theorem depends on definitions:  df-bi 128  df-an 198

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