Theorem nsyl3 588

Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995.) (Revised by NM, 13-Jun-2013.)

Hypotheses

Ref	Expression
nsyl3.1	|- ( ph -> -. ps )
nsyl3.2	|- ( ch -> ps )

Assertion

Ref	Expression
nsyl3	|- ( ch -> -. ph )

Proof of Theorem nsyl3

Step	Hyp	Ref	Expression
1		nsyl3.2	. 2 |- ( ch -> ps )
2		nsyl3.1	. . 3 |- ( ph -> -. ps )
3	2	a1i 9	. 2 |- ( ch -> ( ph -> -. ps ) )
4	1, 3	mt2d 587	1 |- ( ch -> -. ph )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 576  ax-in2 577

This theorem is referenced by:  con2i  589  nsyl  590  pm2.65i  600  cesare  2045  cesaro  2049  pwnss  3933  sucprcreg  4292  reg3exmidlemwe  4321  reldmtpos  5891  fzn  9061