Theorem sylibd 205

Description: A syllogism deduction. (Contributed by NM, 3-Aug-1994.)

Hypotheses

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

Assertion

Ref	Expression
sylibd	|- (ph -> (ps -> th))

Proof of Theorem sylibd

Step	Hyp	Ref	Expression
1		sylibd.1	. 2 |- (ph -> (ps -> ch))
2		sylibd.2	. . 3 |- (ph -> (ch <-> th))
3	2	biimpd 198	. 2 |- (ph -> (ch -> th))
4	1, 3	syld 40	1 |- (ph -> (ps -> th))

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:  3imtr3d  258  ceqsalt  2882  sbceqal  3098  sbcimdv  3108  csbiebt  3173  rspcsbela  3196  ltfintri  4467  copsexg  4608  fce  6189  spacind  6288