Theorem syl8ib 217

Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise.

Hypotheses

Ref	Expression
syl8ib.1	|- (ph -> (ps -> (ch -> th)))
syl8ib.2	|- (th <-> ta)

Assertion

Ref	Expression
syl8ib	|- (ph -> (ps -> (ch -> ta)))

Proof of Theorem syl8ib

Step	Hyp	Ref	Expression
1		syl8ib.1	. 2 |- (ph -> (ps -> (ch -> th)))
2		syl8ib.2	. . 3 |- (th <-> ta)
3	2	biimp 151	. 2 |- (th -> ta)
4	1, 3	syl8 24	1 |- (ph -> (ps -> (ch -> ta)))

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

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