Theorem nsyli 644

Description: A negated syllogism inference. (Contributed by NM, 3-May-1994.)

Hypotheses

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

Assertion

Ref	Expression
nsyli	|- ( ph -> ( th -> -. ps ) )

Proof of Theorem nsyli

Step	Hyp	Ref	Expression
1		nsyli.2	. 2 |- ( th -> -. ch )
2		nsyli.1	. . 3 |- ( ph -> ( ps -> ch ) )
3	2	con3d 626	. 2 |- ( ph -> ( -. ch -> -. ps ) )
4	1, 3	syl5 32	1 |- ( ph -> ( th -> -. ps ) )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 609  ax-in2 610

This theorem is referenced by: (None)