Theorem mt2 184

Description: A rule similar to modus tollens. Inference associated with con2i 124. (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 178	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  188  ax6dgen  1919  elirrv  8130  cardom  8438  0nnn  10663  nthruz  14381  hauspwdom  20593  fin1aufil  21025  rectbntr0  21928  lgam1  24068  gam1  24069  wlkntrl  25371  ex-po  25964  strlem1  27984  eulerpartlemt  29277  nalf  31134  finxpreclem3  31855  konigsberg-av  40171