Theorem nsyl3 626

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 625	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 614  ax-in2 615

This theorem is referenced by:  con2i  627  nsyl  628  pm2.65i  639  cesare  2130  cesaro  2134  pwnss  4161  sucprcreg  4550  reg3exmidlemwe  4580  reldmtpos  6257  snexxph  6952  elfi2  6974  ismkvnex  7156  fzn  10045  seq3f1olemqsum  10503  pcmpt2  12345