Theorem syl8ib 222

Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 1-Aug-1994.)

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	biimpi 186	. 2 |- (th -> ta)
4	1, 3	syl8 65	1 |- (ph -> (ps -> (ch -> ta)))

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:  pm3.2an3  1131  ncfinraise  4482