Theorem sylan9r 390

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 67	. 2 |- ( th -> ( ph -> ( ps -> ta ) ) )
4	3	imp 115	1 |- ( ( th /\ ph ) -> ( ps -> ta ) )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100

This theorem is referenced by:  spimt  1624  sbequi  1720  genpcdl  6617  genpcuu  6618  iccsupr  8835  climuni  9814