Theorem nsyl5 651

Description: A negated syllogism inference. (Contributed by Wolf Lammen, 20-May-2024.)

Hypotheses

Ref	Expression
nsyl4.1	|- ( ph -> ps )
nsyl4.2	|- ( -. ph -> ch )

Assertion

Ref	Expression
nsyl5	|- ( -. ps -> ch )

Proof of Theorem nsyl5

Step	Hyp	Ref	Expression
1		nsyl4.1	. . 3 |- ( ph -> ps )
2	1	con3i 633	. 2 |- ( -. ps -> -. ph )
3		nsyl4.2	. 2 |- ( -. ph -> ch )
4	2, 3	syl 14	1 |- ( -. ps -> ch )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 615  ax-in2 616

This theorem is referenced by: (None)