Theorem mt2 191

Description: A rule similar to modus tollens. Inference associated with con2i 134. (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 11	. 2 |- ( ph -> ps )
3		mt2.2	. 2 |- ( ph -> -. ps )
4	2, 3	pm2.65i 185	1 |- -. ph

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  bijust  195  ax6dgen  2005  elirrv  8504  cardom  8812  0nnn  11052  nthruz  14982  hauspwdom  21304  fin1aufil  21736  rectbntr0  22635  lgam1  24790  gam1  24791  konigsberg  27119  ex-po  27292  strlem1  29109  eulerpartlemt  30433  nalf  32402  finxpreclem3  33230