MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  mt2 Unicode version

Theorem mt2 172
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
StepHypRef Expression
1 mt2.1 . . 3  |-  ps
21a1i 11 . 2  |-  ( ph  ->  ps )
3 mt2.2 . 2  |-  ( ph  ->  -.  ps )
42, 3pm2.65i 167 1  |-  -.  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  bijust  176  19.2OLD  1707  ax9dgen  1723  elirrv  7500  cardom  7808  0nnn  9965  nthruz  12780  hauspwdom  17487  fin1aufil  17887  rectbntr0  18736  wlkntrl  21420  ex-po  21593  strlem1  23603  lgam1  24629  gam1  24630  nalf  25869
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
  Copyright terms: Public domain W3C validator