Theorem sylan2i 687

Description: A syllogism inference. (Contributed by NM, 1-Aug-1994.)

Hypotheses

Ref	Expression
sylan2i.1	|- ( ph -> th )
sylan2i.2	|- ( ps -> ( ( ch /\ th ) -> ta ) )

Assertion

Ref	Expression
sylan2i	|- ( ps -> ( ( ch /\ ph ) -> ta ) )

Proof of Theorem sylan2i

Step	Hyp	Ref	Expression
1		sylan2i.1	. . 3 |- ( ph -> th )
2	1	a1i 11	. 2 |- ( ps -> ( ph -> th ) )
3		sylan2i.2	. 2 |- ( ps -> ( ( ch /\ th ) -> ta ) )
4	2, 3	sylan2d 499	1 |- ( ps -> ( ( ch /\ ph ) -> ta ) )

Syntax hints:   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  syl2ani  688  odi  7659  pssnn  8178  ltexprlem7  9864  ltaprlem  9866  sup2  10979  filufint  21724  pjnormssi  29027  poimirlem27  33436  poimirlem31  33440  pellex  37399