Theorem mt2 612

Description: A rule similar to modus tollens. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 10-Sep-2013.)

Hypotheses

Ref	Expression
mt2.1	|- ps
mt2.2	|- ( ph -> -. ps )

Assertion

Ref	Expression
mt2	|- -. ph

Proof of Theorem mt2

Step	Hyp	Ref	Expression
1		mt2.1	. . 3 |- ps
2	1	a1i 9	. 2 |- ( ph -> ps )
3		mt2.2	. 2 |- ( ph -> -. ps )
4	2, 3	pm2.65i 611	1 |- -. ph

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 586  ax-in2 587

This theorem is referenced by:  0nnn  8650  nn0ge2m1nn  8934  xsubge0  9550