Theorem sylan9r 639

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 418	1 |- ((th /\ ph) -> (ps -> ta))

Syntax hints:   -> wi 4   /\ wa 358

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  df-an 360

This theorem is referenced by:  sbequi  2059  opkth1g  4130  ncfinraise  4481  funun  5146