Theorem syl8ib 234

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	biimpi 168	. 2 |- (th -> ta)
4	1, 3	syl8 27	1 |- (ph -> (ps -> (ch -> ta)))

Syntax hints:   -> wi 3   <-> wb 163

This theorem is referenced by:  pm3.2an3 1049  ee3bir 1274  en3lplem2 5757  iscnp3 14946  fictb 15371

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 164

Copyright terms: Public domain