Theorem nsyl3 627

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 626	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 615  ax-in2 616

This theorem is referenced by:  con2i  628  nsyl  629  pm2.65i  640  cesare  2149  cesaro  2153  pwnss  4193  sucprcreg  4586  reg3exmidlemwe  4616  reldmtpos  6320  snexxph  7025  elfi2  7047  ismkvnex  7230  fzn  10134  seq3f1olemqsum  10622  pcmpt2  12538  elply2  15055