Theorem nsyl3 621

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 620	1 |- ( ch -> -. ph )

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:  con2i  622  nsyl  623  pm2.65i  634  cesare  2123  cesaro  2127  pwnss  4145  sucprcreg  4533  reg3exmidlemwe  4563  reldmtpos  6232  snexxph  6927  elfi2  6949  ismkvnex  7131  fzn  9998  seq3f1olemqsum  10456  pcmpt2  12296