Theorem sylan9r 408

Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 5-Aug-1993.)

Hypotheses

Ref	Expression
sylan9r.1	|- ( ph -> ( ps -> ch ) )
sylan9r.2	|- ( th -> ( ch -> ta ) )

Assertion

Ref	Expression
sylan9r	|- ( ( th /\ ph ) -> ( ps -> ta ) )

Proof of Theorem sylan9r

Step	Hyp	Ref	Expression
1		sylan9r.1	. . 3 |- ( ph -> ( ps -> ch ) )
2		sylan9r.2	. . 3 |- ( th -> ( ch -> ta ) )
3	1, 2	syl9r 73	. 2 |- ( th -> ( ph -> ( ps -> ta ) ) )
4	3	imp 123	1 |- ( ( th /\ ph ) -> ( ps -> ta ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106

This theorem is referenced by:  spimt  1729  sbequi  1832  updjudhf  7056  genpcdl  7481  genpcuu  7482  iccsupr  9923  climuni  11256  tgcn  13002  metrest  13300