Theorem syl8ib 166

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 120	. 2 |- ( th -> ta )
4	1, 3	syl8 71	1 |- ( ph -> ( ps -> ( ch -> ta ) ) )

Syntax hints:   -> wi 4   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm3.2an3  1178  necon4bddc  2438  necon4abiddc  2440  necon4bbiddc  2441  necon4biddc  2442