Theorem mt2 179

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 11	. 2 |- ( ph -> ps )
3		mt2.2	. 2 |- ( ph -> -. ps )
4	2, 3	pm2.65i 173	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  183  ax6dgen  1768  elirrv  8012  cardom  8356  0nnn  10556  nthruz  13835  hauspwdom  19761  fin1aufil  20161  rectbntr0  21065  wlkntrl  24226  ex-po  24819  strlem1  26831  eulerpartlemt  27936  lgam1  28232  gam1  28233  nalf  29431